I wouldn't say games are robustly divided into guy or girl games, because the video game industry is another form of entertainment. It's like saying "Friends" the tv series are for girls, but in reality, it just good entertainment. While there are "chick flicks" in movie industry, "chick games" reallyhaven'testablished itself in game industry. There are those games that cater to young girls like Barbies horse adventurethats beenmentioned above, but those games are more for people with less coordination skills. I honestly believe any games can be for girls or guys, as long as there are people who are willing to give the games a chance. Now all said and done, here are my recommendations for you to try with genres.

First person shooters

Half Life 2: This is a great shooter with awesome story line, and I highly recommend it to anyone. The character development is there and the strong female lead makes this game bring up extra layer to the game.

Halo 1 and 2: This is also a trilling shooter game that was created buy bungie, and single player really shines here, but the game excess at the multiplayer. Very competative game in multiplayer, and very intriguing single player.

Unreal Tournament: All of the UT series is fast and fun in multiplayer mindless shooting, but can get complex with domination mode. If you want something less than intimidations, i would suggest this game.

Counter Strike: This is an awesom squad base game, but it really requires bit of a teamwork. If you want to play with your friends then try this game, but watch out for elitist, since they will hammer you for making a simple mistake.

Strategy games

Tetris: every and all incarnation of this series are addictive, and that is all i have to say about this game.

Roller coaster Tycoon: If you like sims, then you might like this. Your task is to make a best roller coasters for your "sims"

Mahjong: I don't know how to play this game, but i hear it just plain fun strategy games for everyone

Real Time Strategy

Starcraft: Fun game that will never get old, and hasbalanced race and very competative online multiplayer. strongly recommend and cool story in single player campaign

Command and Conquer: great cutscene and interesting story, enticing multiplayer

warcraft 3: 4 balanced race, and great single player campaign. Enjoy the multiplayer

Rome or Medieval Total War: Control vast armies and manage ecomony while holding your city from reballions. Has great political intrigue and very interesting and complex strategy in realtime.

Company of Heroes: Great RTS in the WW 2 setting, very rich in game play and awesome story telling

Warhammer 40k Dawn of War: Fun Series and awesome multiplayer game

MMORPG

World of WarCraft: Can't stop playing

Guild Wars: Free Online game

City of Heroes, or City of Villian: If you ever wanted to be a superhero, this game makes it happen. You can be anyone and everyone you like to be as a superhero. I mean anyone.

RPG

Diablo: great 2d rpg game, and addictive game plays, can be played multiplayer online

Elder scroll: great 3d game, with immersive single player

Final Fantasy: awesome story telling and the series never get old.

I hope you check one or two of the titleI have listed, and hope you like them. :D