My Favorite Game is a tough one to think about, considering I haven't played as many as most people, but as far as my current favorite:
Well, I guess it has to be Chrono Trigger. The more I think about it, the Quantum Leap/Back to the Future/Sliders aspect of the ability to travel through time is always amazing to me, and what makes it amazing beyond most games isn't the ingenuity of the class levels, or the worlds (which, even in its SNES Graphics are beautiful), or even the characters or the various endings, it's that it's story spans over various centuries, and everyone of them tells a story.
Yes, I love Metal Gear Solid, but Chrono Trigger is ingenious in its delivery, it's less difficult to follow, and its beautiful.
2nd Best: Earthworm Jim
3rd Best: Earthbound
Honorable Mention: Metal Gear Solid 3.
As for Least Favorite:
This is kind of a difficult one, but my least favorite game of all time (so far) is:
Celebrity Deathmatch. It's the only time I've ever played a game that was cursed. A friend of mine loaned it to me, I played it one rainy evening, my stomach started killing me. The game sucked, I felt like I was being stabbed in the gut, and Nothing I did made me feel better. Hours after the game was shut off, I couldn't sleep without being in pain. Found out the next day (about 15 hours later) that I had an ulcer (at 13). Today, it is a cursed game, and I never show much sympathy to it anymore.
2nd Worst: Enter The Matrix
3rd Worst: Spice World (Yes, Shut up).
Honorable Mention: Jersey Devil (For the Playstation 1. Look it up, it's just...just awful)