Yeah. I know it's like that in some countries. It's nice.

Sounds like someone who doesn't understand EULAs read one for the first time in his life and didn't like the "lawyer" talk. Like many people have said already, the law on this subject hasn't changed for years. You can use some other method if you like, it's not going to change.
The way it's written is just to say that you don't own the ideas, assets, etc. that are contained on the disc, download, cartridge, etc. It's just a fancy way of legally protecting the Intellectual Property. They don't want people to buy the game, use their assets, and then pass them off as their own creations.
So, yes, you don't "own" the game, in a sense. Just like with software like Maya, 3DS Max, and Visual Studio, you buy a license to use it. Same with games. It's just that games haven't had the "1 license per 3 computers" deal until recently, which is where DRM comes in.

There. Fixed that for you.
:)

Thank you. Yeah, I guess licenses don't generally go on a "per computer" basis.
I do realize though that I'm probably about the 5th guy to say this.
I think we've beaten it to death quite a bit. If you don't want to accept the fact that this is how it's been all along, then that's a shame. But there's nothing I can do about that.
I'm sure there's a lot of other people out there who misinterpret legal documents as well. Hell, if we didn't, we wouldn't have a need for lawyers now would we. :Þ
I'm quite sure GOG will take off just fine without one or two people.
For the rest of you, enjoy some Good Old (damn) Games.

So do I actually own the game or not? Is GOG lying or not?
The EULA says I don't own it, the website says I do.
Which one is lying?

Sigh... which way do you want it? What we've been trying to tell you is that no, you have not been lied to. Ownership in this instance means two different things. GOG uses one meaning and the EULA uses the other. GOG uses the term for consumers and the EULA uses the term for lawyers. GOG's meaning of ownership is that you can use the game however you want as long as you don't pirate it, make copies to sell to your friends, basic common sense stuff. EULA's meaning of ownership is that you own everything about the game and can sell it, edit it, rename it, do whatever you want with it because you created the game or bought the Intellectual Property for it.
By GOG's definition, do you own it? Yes!
By the EULA's definition, do you own it? No!
Seriously, pull out an older boxed retail game and find the EULA and you'll find it similar to the one from GOG. This is how all computer software works.

I think I made a mistake in originally guiding this discussion to a debate on the semantics of what ownership means for digital goods, and specifically, what it means for goods that are tied to an account. I maintain that speaking of "ownership" in regards to the limited rights that a consumer has to software which she or he "purchased", even with respect to legal language, is not a misnomer. To back this claim up, I would point to the EFF article that I cited in one of my previous posts which essentially concludes that transactions which appear similar to sales do in fact grant consumers the protection of a sale, which includes the right to resale.
I would also cite the 1997 Novell v. Network Trade Center case which, is summarized nicely at wikipedia
But like I said, I wanted to get away from the semantic debate of what it is to own, so from now on I'll try to speak of "title to" games rather than "ownership of".
Anyways, there have been half a dozen posts since I started putting this response together, but let me try to respond to a few of the big arguments:
No, it's not.
I'm not simply referring to the existence or not of EULAs (although I do not believe that they were as widespread "back in the day" as they are now, and sadly, my mother threw many of my old games/boxes out when I moved to college, so it would be difficult to check), but rather to the enforceability of EULAs as compared between games from back in the 80s-90s and games distributed online now.
For instance, as recently as the 1990's, you could go to a store and rent PC game. I did this in my hometown growing up, and just to make sure my town wasn't a fluke, I checked some old newsgroup discussion on Google, and sure enough, many other people were doing this:
http://groups.google.com/group/iinet.general/browse_thread/thread/56d23a1bc0e055a7/fcf82856a8bf8358?hl=en&lnk=st&q=rent+pc+games#fcf82856a8bf8358
http://groups.google.com/group/van.forsale/browse_thread/thread/708a0373a5ae13be/e53b762096e6d156?hl=en&lnk=st&q=rent+pc+games#e53b762096e6d156
http://groups.google.com/group/alt.games/browse_thread/thread/7a89aa393e9b9a2f/bb000874f15773e9?hl=en&lnk=st&q=rent+pc+games#bb000874f15773e9
Personally, I have no intention of renting games out, and with the prices that GOG is selling at, I would be out of business. My point is that the consumer rights were much higher back in the day.
What ended this era of rights was not the move to internet-based modes of distribution, it was the set of laws that made circumvention of DRM technology, illegal, even when such attempts at circumvention were for legal purposes, like trying to get a DVD to work on Linux or trying to set up a new game of Spore for your daughter to play with.
While someday, there may be a landmark case that establishes that I do in fact have title to games distributed via the internet, I have not seen that case yet, so my rights remain uncertain when restricted by the EULA GOG uses.
Additionally, even if many of you are right and I never had the rights I imagined, who cares? As a normative issue, I ought to have the right to let my friends play the games that I buy when I'm not using them. Under the terms of this agreement, that can never occur.
In an earlier post, I granted that their are some challenges, but they are by no means insurmountable.
From a technological standpoint, it would not be difficult in the least to add a button to the "my accounts" page which says "I've sold this title to another person, please remove this game from My Account".
From a business practicality standpoint, I believe that such technology would actually be a net plus for several reasons.
First of all, such a feature would not promote piracy. Given that GOG is true to their word insofar as the executables contain no DRM, anyone inclined to pirate the works they download probably already is. Adding a remove-game button simply provides a mechanism for honest users to be honest when they're giving the game to someone else.
Secondly, allowing transfers provides an incredible viral marketing opportunity. After a customer has removed the game, GOG can follow up and ask for the email address of the new title holder. They can then send an email to that person, inviting them to activate their account so that they make take advantage of the online download for the game they recently purchased, and so they can enjoy other games.
I think that the marketing potential outweighs any lost sales. Even if it doesn't, it treats the customer with respect.
A contract negotiating perspective is the hardest - I understand that publishers like Interplay are going to be hard to convince to not only give up DRM, but also to do so without at least a pro-forma nod to the licensing scheme the games industry has become accustomed to. Ultimately though, Interplay really isn't selling that many copies of Fallout (much less Battle Chess Special Edition) so even the limited sales that GOG can offer give them a big bargaining chip.
Because I love games, especially on a PC, and I believe that for the art of games to grow, you must be able to share.
Again, I don't mean share as in make available for millions of people to download, I mean share as in letting a friend play. I got into games, at first casually, when my friend shared a massive collection of Apple II/e games with me. I truly became a "hardcore" gamer when my friend gave me his copy of Half-Life. I have since dumped literally thousands of dollars into the industry, both on the latest and greatest games, and in finding old classics to play through. What has largely kept those old classics around are not the $99 new copies of Monkey Island that someone kept in a vault, instead, they are the $15 used copies people are kind enough to sell.
While it's great that GOG keeps new copies of many of these games available at low costs, there's a chance that when it comes time to renew the contract with Interplay in a few years, they may need to change their selection, or they might simply stop offering some games because it's not worth it to host a game that just didn't sell well. What is sure to keep good old games (note the lack of capitalization) being played are transfers to new gamers, and it would be unfortunate if Interplay had the power to decide those transfers should be stopped.
I've been writing this for a while now, if there are any points that I missed, let me know.
PS - the forums should really have private messages.

And you all kept saying 'why don't you understand?'
Every post I've made in this thread has been a positive contribution to this thread, regardless of whether or not it was insane or purely understandable. This is an issue that needs to be escalated.
What do you think would happen if you read on Kotaku, or Joystiq, or even in a webcomic that's well regarded, that GOG is lying? That you don't own the games?
This needs to be addressed.
I understand full well both sides of the argument, I play devils advocate. Because it needs to be painted clearly, much clearer than what has been painted, as to what you can and can't do. There have been a number of threads of people confused with whether or not they could legally post items they bought here, on other websites.
This thread, while dirty, nasty, and ugly, was necessary because it was not clear.

Actually, this is something I've been very curious about with Steam, and by association, GOG. Both Steam and GOG (and Impulse, I think) offer unlimited downloads of the games you have purchased for as long as you want. This is very different from all the other digital distribution sites that usually only allow you to download your purchased game within a 3-6 month time period.
How are Steam and GOG able to do this? It sounds like they have some sort of unlimited distribution contract. If Interplay wanted to stop distributing their games here, how would that work? Do they only stop selling the games to new customers while still providing them to those that have bought it already? Or will they even delete the games off of people's accounts (unlikely)? Or maybe they can't do anything because GOG has unlimited distribution rights in their contracts?

Ok, this may have already been said, but I will say it anyway.
What GOG mean by no DRM is this: There is no software trying to stop you, like Star Force or SecurerROM. That is all it means. You relay thought they were going to let you do ANYTHING with it? lol, that is pretty silly.
TBH, I don't read it. I know what most of them say, and I never plan to do anything except play it, and maybe make a mod, if I get an idea.

ValvE has had to rely on some advertising revenue recently for the older titles. Whether that is to feed the master servers for the older titles or not, I am unsure.

Distribution rights permit the sale of the game to customers. They have nothing to do with supporting existing customers. If you have bought the game from GOG, then you legally own it, and GOG can let you download it at need.

I think this has been blown out of all proportion. This has been the way most software has been sold and always will be sold. It is just a shame a few people just want everything and still some more.
All the Eula basically says is that you do own a copy of the game to do with as you please for personal use, but you do not own the IP or art assets, etc.
You can redownload the game all you want, you can burn it to a N+1 CDs/DVDs, you can reinstall it N+1 times. you can install it on every computer you have. You get free extras and extended support. What more could people possibly want?
I for one will keep buying games from and supporting GOG for the freedom that old games used to come with in the good old days.
I won't be buying the Electronic Arts (and other companies) "You're free to do as we tell you" bollocks.
edit: spelling.

I really do wonder if unlimited means unlimited, I think I'm going to download the titles I've bought as much as possible, to my own computers of course, and see if anything happens.

The problem is that the EULA is phrased in a "you're free to do what we tell you" manner. I have been harping on the right of transfer because once you have that right, the other restrictions, beyond those articulated in national and international copyright law, go away. At the same time, the other restrictions are just as frustrating. For instance, yourheadquake wanted to use a fan made Italian translation (forum post here: http://www.gog.com/en/forum/Fallout_Series/a_matter_of_language_and_gog_game_developer_of_fallout_italian_ile_exe/8 ) Under the EULA, the simple answer is that he may not. The relevant section reads:
You may not transfer, distribute, rent, sub-license, or lease the Program or documentation, except as provided herein; alter, modify, or adapt the Program or documentation, or portions thereof including, but not limited to, translation, decompiling or disassembling.
(Emphasis added)
Many people are right that most modern games contain similar restrictions. However, the first sale doctrine protects me from those restriction by granting me the right to transfer on terms outside of the EULA. There are two ways that I lose those rights and am again forced into these restrictions:
1: The company uses DRM, which is illegal to circumvent and which locks to title to my personal information. (Thank you GOG for not doing this!)
2: The company offers perpetual access through the internet, which makes a complete transfer and/or destruction of all copies impossible. (Case law hasn't caught up here.)
Someone asked earlier what I thought the spirit of offering games with no DRM was. In short, I believed it was to restore to gamers all rights, except for those specifically restricted in copyright law. If that isn't done, gamers who want to play through in their native language or who want to let their friends play lose out.
Edit: The quotes were mangled