Personally, I don't want companies to try and make their games appeal to me as a woman. I want them to appeal to me as a gamer. I don't need Hello Kitty or Barbie or a box plastered in pink to get my interest. What I want is something that plays well and has a story (or something about it) that keeps my attention.
My own tastes vary. I started gaming in the 80's on my Amiga 500, so that may influence some of my preferences.
FPS: Used to play a lot - and I do mean a LOT - of Doom, Quake and Hexen back when I was 16. Which is a lot longer ago than I really care to admit. Nowadays, I enjoy things like Mass Effect or Binary Domain, but not so much CoD or Battlefield. Not because I hate them, but purely because I find the realistic shooters boring compared to shooting aliens or robots and the like. Real war doesn't interest me. Blowing up a Reaper, does.
RPG: Probably the motherlode for me, right here. Early ones include Cadaver, Ultima, Dungeon Master, Eye of the Beholder and Ishar. Nowadays I'm more of a Final Fantasy / Dragon Age / EverQuest kind of girl. I don't know what it is about these, but I just adore the mico-managing, boss killing, level grinding, epic story-ness of a good RPG. I can happily lose myself in them for hours. Days. Often longer.
Adventure: I adored the point and click adventures of years ago. Day of the Tentacle, Monkey Island, Lure of the Temptress... Oh, those were the days. Modern adventures have moved on a lot, I suppose Assassins Creed and Uncharted are the franchises that spring to mind here. I like those, too, though they're not the same as the old stuff. That's not to say they're bad or that I don't like them. But adventure games now and adventure games then are two different animals.
Platformers: The old ones like Rainbow Islands or Zool got a lot of playtime, but once they started moving over to 3D I kind of lost interest. 3 lives or you're out, though. Blimey, kids these days don't know how lucky they are...
The rest: Well, I've got and played some Sims. I think that's practically mandatory these days.

But I also very much enjoyed the Populous series back when they were out. I thought Portal was excellent, and Guitar Hero passes an hour or two now and then (I hit things with sticks). I own a copy of Dance Central, though the curtains have to be closed if I'm going to attempt any of
that. Bayonetta, God of War, Batman, Heavenly Sword... Put it this way. Between my fiance and I, our computer room has more tech and titles in it than the local GAME shop (yes, it's still open boys and girls).