It all depends on the type of game, an arcade style game certainly doesn't need Crysis level graphics to be fun, and having them won't necessarily make a better gaming experience, but for most other types of games better graphics will improve gameplay experience.
Your enjoyment of any game will improve with better graphics. People say Minecraft proves you don't need realistic graphics to have a good game, but I played it quite a while in the default settings, and eventually decided to add a higher definition texture pack, which rocketed my enjoyment of the game immensely, for the first time I stood and gawped at the sun rise, for the first time creepers looked properly creepy and abominable, zombies looked horrifying, whereas before they were just threatening blocks. My buildings and creations looked far better, my houses cozier.
My immersion skyrocketed with that update in graphical fidelity, and I experienced exactly the same thing (to a slightly lesser extent) When improved Skyrim's graphics.
Look at the mods for Skyrim, the top ones are pretty much all graphics mods for higher textures, and the popularity of Minecraft HD texture packs. Clearly there is something to be gained from having better graphics.
DISCLAIMER: Of course, if your game is pants then having flawless graphics will not turn it into a great game, but it does have it's importance in issues of immersion and appreciation.