I can't play a game unless it has good graphics (graphics in terms of quality/resolution). If a first person game is pixelated I can't play it. I don't mind if a side-scroller game is pixelated because they don't really need graphics to improve their game play and good graphics may ruin side-scrollers. It may confuse you with whats in the map and whats in your way etc... In my opinion, Minecraft got lucky with the fact their game has two basic tasks yet they have been turned into something much more by their community. Nobody seemed to care about the graphics but now shaders exist so it doesn't matter anyways.
I was watching this video which compared Halo 4 graphics to Battlefield 3 graphics (both on current gen consoles) and were about 1 or 2 years apart with Halo 4 being the newer game. I was so amazed by how great the Halo 4 graphics were, I had never really noticed because I was always focused on the gameplay. Halo 4 is another game whhere graphics don't matter, in this case it's because the community love the game, many Halo fans still play Halo 3 and enjoy it despite it's graphics. Battlefield is a game which has to have decent graphics to be playable, especially with its huge maps and 64 man servers. Gameplay is good but without the good graphics it wouldn't be what it is.
Keep in mind these are just opinions.