The number one most important factor to me is FUN.
e.g., people sometimes criticize the wii for not having graphics as other consoles. But if the wii has new super mario bros or mario kart, and other consoles don't, then to me, the wii wins because I find these games to be the most fun.
Second comes gameplay, but I guess this is covered by fun...?
Then it's the visuals. This does not mean graphics. It doesn't have to look flawless and realistic. It just has to look nice. Nice colours, cute characters etc.
Fourth is replay value. Whilst this isn't essential in every game, being able to play the game for a long time certainly is appealing. It's why I love animal crossing.
Video games, in terms of what they look like, have very little to do with imagination. It's pretty much there for you to look at. There isn't anything to imagine, it's not like with books where all you have is a description. Graphics are as important as anything else.