I'm new to gog.com, I haven't been around much so I don't know if this is the best place to ask.
I won a free game code to this site for any game I want (from USAToday) but I cannot make up my mind. I was thinking maybe the community could give me some insight on what would be a good game to get (or just list your favorites).
I already have:
Prince of Persia: SoT
BG&E
Ground Control
I like fighting, shooting, action, puzzle, mech, adventure, and simulation games. I do not like RTS games, but there have been a few times before where a good RTS game will appear and I'll like it (very rare occurrence though). Machine Specs are not a problem as my machine can run everything without breaking a sweat (so to speak).
NOTE: I cannot play anything that is extremely bloody/violent/suggestive as my brother likes to watch me play games and I rarely have time to play these kind of games when he is away. So it would be best for me to play something that is also good for him to watch.
Here's a list of games I'm currently considering (feel free to suggest):
Evil Genius (I only watched a trailer, is this like the sims or something?)
Fallout (is this series something I would enjoy?)
Fallout 2
Shattered Steel (Is there a graphics patch?)
Colin McRae Rally 2005
Broken Sword 2 (Is this really that violent? It looks very cartoony)
Unreal Tournament 2004 ECE (for the times I ever get to play alone)
Earth 2160 (looked interesting)
It would be fantastic if you guys could help me out! Thanks!

Try the Fallout demo, http://download.cnet.com/Fallout-demo/3000-7539_4-10008318.html. I loved them personally and think they would make a fine addition to any collection provided that you read the manual or figure everything out.
Aside from your list I would highly recommend Duke Nukem 3D. The game is (in my opinion) the best shooter that GoG has and the most fun for sure.
Edit: In Duke there is a parental lock. Never used it but I can assume it would make it playable with your brother in the room.

I probably wouldn't recommend the Fallout games if you're worried about your brother watching you play anything adult-oriented. Although you can turn off most of the graphic combat violence in the options screen (the default is extremely gory at times), there's still a lot of dark, violent, or suggestive imagery at work.
Note that these games are very much old-school computer roleplaying games, which you haven't mentioned liking in your OP, but if you enjoy that type of game and think you can keep them away from your sibling, you'd be hard-pressed to find better.

I'd recommend Evil Genius, then Fallout (after you try the demo as Whiteblade recommended).
Evil Genius only really has cartoon violence, and focuses upon base-building and research trees. If you remember Dungeon Keeper, its been likened to that. I suppose also if you enjoy the kitsch side of Bond movies or the Austin Powers parodies, then its right up your street.
Fallout is a little bit more complicated, because its a universe to get immersed in, not just a game. Its exceptionally dark, but you can turn down the visual violence. It involves lots of reading of dialogue, but every bit is worth it. The combat system is turned based, so you can really think about what your going to do, plus the characters are great as well.
Anyway, that's what I think.

Since you like action games and shooters, I can recommend the free-floating underground combat of Descent 1+2, or the platform action of Earthworm Jim 1+2. Both are great deals, and should be fine for your brother to watch. There's a small amount of animated blood in both games, lots of explosions and scorched metal in Descent, and cartoon violence and slapstick in Earthworm Jim.
Be warned that EWJ may be difficult to play if you don't have a gamepad.
By the way, Sacrifice is a great RTS for the gamer who doesn't like RTS games.

I got into GOG because Fallout, and have bought several more games since then. However, what's keeps me entertained more often than not is Pro Pinball Big Race USA.
Shame I missed getting the Pro Pinball Fantastic Journey last time there was a sale; but I plan to get it soon.

The Broken Sword games are point and click adventures and as I recall, BS2 wasn't exactly violent.

I'd recommend Fallout but it's a CRPG, and not of the action kind. The combat isn't really stellar but it isn't the focus of the game, and it even provides you with options to bypass most fights, so if you only want to kill stuff, you should look for Duke Nukem 3D, Unreal Tournament — the first one is the best but UT2004 deserves an honourable mention — or Painkiller.
It's a game, just like any other. They all rely on immersion.

I'd go with Broken Sword II. There are a few murders, but not enough to make it an extremely violent game. It's more of an Indiana Jones movie. I feel it has the most compelling story out of all the GOG games, and when you combine amazing story with point-and-click, the result is almost always spectacular.

I'll definitely favorite it for the next time I need to choose something.
Yeah, but Painkiller and UT2004 and Duke Nukem would be games I would have to play on days that my brother isn't around.
That's what I thought judging from the screenshots.
I looked into Sacrifice today and I wasn't amused much by the summery. I've played Earthworm Jim before (on the GBA) so I feel like I've been there done that.
Someone suggested Freespace 2, I got rid of my joystick for my computer a long long time ago and the keyboard controls were really confusing. It looked fun, but it was definitely as game for people with computer joysticks.
I think I'm gonna go with Evil Genius. I played the demo and loved the base building concept. It's actually really fun to play and I'm amazed that I like it. Thank you all for the suggestions (great for building my list up for next time)!

I haven't played Freespace, but I play Descent with the keyboard. It takes some experimentation to get the controls down, though.

Good choice matey.

That was in reply to Skreczi but at that point, I was tired of quoting everyone (plus I didn't go back to check who suggested it). I've tried Freespace. There are some cool mods being built on the engine (Starfox) but the game itself is hard to control.