My favorite is Sonic the Hedghog Triple Trouble.
Reason(s): One becasue this was my very first Game Gear game I ever owned. Second, it took me a long time to beat it. Ever since I was 5 years old, I've tried my best to beat this behemoth. I eventually did it when I was 20 years old. Yes, it took me 16 years to beat this game with Chaos Emeralds in hand with both Sonic and Tails. No game, except Majora's Mask, has eluded completion from me for that long. You could say it was quite the Moby Dick to me and it was driving me crazy not beating it. It has a lot of nostalgic memories dear to me and I'd play it any day. I downloaded the 3DS port because...that's how much I love it.
I also have an obscure favorite. More like a guilty, very guilty pleasure.....I'm talking about, Shadow The Hedgehog. Now before you press that quote button, let me explain.
I hate this game with every bone, nerve, and drop of blood in my body. It's dull, it's boring, it's repetetive, it has a pointless concept, but there's one thing that's really fun to me in this game. The gunplay. I love the gunplay. Just shooting everything in up in my path is pretty awesome, epsecially when I get infinate ammo with chaos power....but it's still bad...Oh and it's inconsistant too.