Let's talk about old games, that are almost impossible to get running on modern systems.
One example that comes to mind would be Discworld Noir, which is very difficult, if not impossible, to get running on any OS newer than Windows 98. At least I've only managed to get in run by using Virtual PC installed Win98 after I've had WinXP machine.
Heck, I've even tried to get the game running by using Wine under Ubuntu, but at least for now Discworld Noir won't even start under Wine's newer version. At some point in time I managed to get the title screen of the game visible, but then they did something to Wine and the game stopped working all together.
I've understood, that most problems with Discworld Noir come from old copy protection system, which is some old, obscure and deeply broken CD check, that just doesn't work on newer systems. Also, the game doesn't seem to like newer hardware, as some people have gotten it working under WinXP.

Blood Omen: Legacy of Kain, Warhammer: Shadow of the Horned Rat and System Shock 2 all have their particular quirks which make them difficult or impossible to run depending on your OS.

Not sure about the other two but you can get System Shock 2 running on any OS through mods and tweaks.
The only games I haven't been able to run on Win7 so far are Metal Gear Solid 2, which is incompatible with modern sound cards period, and Tex Murphy Overseer DVD version.

The windows version of Dungeon Keeper.

I would love to see Interactive Magic's Malkari run on current systems.
You can get to the menu but after that nothing.

Black Mirror. I have the original CD's, and it's im-efing-possible to play it. Even tried some crack and burn solutions, but it made it playable for like ten minutes, before kicking me out and throwing all my clothes out the window(s XP) .

Yeah, Overseer DVD is a difficult case. You can get working under WinXp, but after a certain point it just keeps crashing and the game turns unplayable.
But I remember seeing some info about it, as it's mostly related on DVD coded the game uses. Some one got the game working after re-decoding the movie files with newer codec or something, but it takes some effort.

I got it working on my girlfriend's Vista 32bit laptop, but I couldn't get anything working on my Win7 64bit machine, and I have no idea how long it would have worked on her machine without hitting problems.
Even the CD version is a pain due to the 16bit installer not working... I copied all the files over but it never finds the CD2 files for some reason. I gave up and just decided to buy it on here.

Personally I could play Overseer DVD version as far as the Indian (Anazari or something like that) caves, after which the game always crashed. Then I managed to, with a sheer amount of patiance, get over that only to get another area, in which everything failed and I just gave up.
Besides the DVD codec issue the game also has some pretty bad graphics issues as well. I think to get it working properly under new equipment and OS's requires some pretty good luck..

One other game I would dearly love to see run is Acclaim's Machines, (a.k.a. Machines 3D).
This is such a good RTS and has so many fun units to build and modify. For the age it even allowed first Person control over any unit you wanted at any time.
This sort of runs now, but not without issues. I wish GOG would get this game and make it work; it is a blast to play.
As I understand there are no cheat codes for the game whatsoever, and some levels are very challenging for sure.
This is one Great, Good Old Game!

They already had a license for a 16-bit installer, and would have to shell out a boatload of cash for the license to a 32-bit version?

Hey, at least you can get around the installers most of the time. When we go past 64bit architecture then what are we going to do about the games themselves? Ack!
I hope GOG is still around and has some genius idea!

I have never had any problem with the Windows version on XP on a modern system. There have been some problems with Vista and Win 7, but there are work arouns that seem to help a lot of people.
ANyway, there is always the DOS version of both DUngeon Keeper and the Expansion,and they work fine under DOSBOX, so it is not really a biggie. BTW the DOS and Windows version are exactly the same.
You can't use the 3D acclerated version in DOS, but you are not missing much (the graphics are only slightly improved) and most modern Video cards don;t like the acclereted version anyway.

Been trying to get my Urban Runner game to work but haven't managed to get it to work. If anyone have tips do tell me :)