*looks at the "Barbie Horse Adventure" type answers and sighs in dismay*
Containing no Y chromosome myself, some suggestions I would throw out (which have probably already been mentioned ad nauseum, but I'm too lazy and tired to check, include:
Kingdom Hearts
Animal Crossing: Wild World
Katamari Damacy
Okami
Scribblenauts
Portal
Legend of Zelda: Twilight Princess
Plants vs Zombies
Super Smash Bros Brawl
Cooking Mama (tell her you're not trying to get her into the kitchen or anything, it's just a fun little game

)
Rayman Raving Rabbids series (if she likes goofy cuteness)
Arcana Heart (modern old school fighter with all Japanese girl characters, if that made the slightest bit of sense)
.hack//infection
Ico
Bookworm Adventures (then again, I like word puzzly type games)
Guild Wars
Neverwinter Nights
Professor Layton and the Curious Village
Princess Debut (ok, it's super super girly and a little juvenile, but it's part little Elite Beat Agents knock off, part dress up Japanese dating sim and it makes me happy, plus it's got these great little versions of public domain and classical songs)
Wii Sports/Wii Sports Resort
Prince of Persia (not the new one, hell no)
Tetris Party (wiiware download)
Tetris DS (Brentalfloss knows; women love Tetris)
Mario Kart Wii
Psychonauts
Bomberman DS
Samba De Amigo
Pokemon Diamond or Pearl
Mystery Case Files: MillionHeir (hidden picture game)
*opens up game drawer to check to see if there's any she forgot*
DDR
Guitar Hero/Rock Band
Karaoke Revolution/Singstar if she likes to sing
Looking over this list has made me aware of a few things:
1. Yeah, I'm broke and don't own many consoles (PC, DS, Wii, PS2, that's it)
2. Not many of these are actually "artsy" but are all fun in their own way
3. Yeah, some of these titles may seem juvenile or basic, but if she's new to gaming, you don't want to intimidate her with complex controls (ok so that rules out Arcane Hearts combos, but whatever). You just want her to have fun. The top seven on this massive going to bed procrastinating list should be great.
4. I'm tired and need to go to bed