I don't mind anime based on games...it depends on the game, really, and how far the show adapts it.
Hyperdimension Neptunia: The Animation was both fantastic and disappointing - fantastic because it captured the essence of the games perfectly, but disappointed because it tried to do all three games in twelve episodes, which made it feel disjointed and random; it couldn't quite seem to make up its mind whether it wanted to be an adaptation or an original work...which might have been intentional, thinking about it. xD
Sengoku Basara: Judge End wasn't as good as The Last Party, which I thought was pretty weird. Both adapt the third game, but take slightly different views on it - the show focused on the characters who never got any notice in the first two seasons. I was very happy to see Tsuruhime, amongst others, but they took the dull ending route. The Last Party, by contrast, focused on the main four characters to the exclusion of everyone else...but it took the ending route where Nobunaga comes back from the dead, and I LOVED that ending in the game. Plus Nobunaga is voiced by Norio Wakamoto, which should be self-explanatory. It felt more epic in scope and conveyed more of an essence of the game - plot is secondary; all that matters is flashy moves and dramatic dialogue. The Last Party had that in spades. Judge End didn't.
Tales of Symphonia: The Animation was terrible. It didn't do the game justice at all...and it took FOREVER to come out. The Phantasia animation was a fair adaptation of the game's story, though - Phantasia took a long time to explain things. The anime launched right into it and felt a lot more epic in scope. I've not watched the Abyss anime and I don't plan to, although I will watch the Vesperia and Zestiria prequels somewhen.
Typically, I like to play the game first, so I'm familiar with the source material...it prevents game spoilers, which are far more damaging than episode spoilers to me, as I will (or should be) playing the game longer than watching the show. I haven't watched the anime adaptation of Atelier Escha & Logy yet for this very reason...plus I'm still holding out slim hopes for a dub. xD
...oh, and Dragon Age: Dawn of the Seeker is the WORST anime film I have ever seen. It's one of the worst anime I have ever seen, in fact. I'd probably rather watch Chaos;Head again than force myself to sit through that again. Much as I like Cassandra as a character...gods, what were they thinking. Western games do not make good anime. Not even when they're as good as Dragon Age. That said, the Dante's Inferno movie was interesting for it's varied direction in art style...but it was pretty mindless, and not very subtle. The game itself was more than just a God of War clone, but the anime didn't portray it as such, which was disappointing.