I've got a lot of games I love. Here are some that few people have played and may (or may not) have heard of:
Freedom Force - It's a real time, tactical, super-hero game. It's just so much damn fun. It's the only game I've played where you can control your own super hero team. Well, that and the sequel. A lot of love went into making this game. It pays homage to Silver Age comics like the ones written by Stan Lee. There was, for a good time, also a fan community that made a ton of optional content for this game (i.e. including a lot of stuff that was IP protected). That also added a lot of extra life to a game I already loved to death.
Heroes of Might and Magic 2 - Occasionally I will find someone who really likes HoMM3, but I don't think I've found a person in the past couple of decades who has even played HoMM2. Personally I think this game is the better one on the single player side. (HoMM3 is a lot more balanced and therefore much better for multiplayer.) Before I encountered this game, I had played several fantasy strategy games like Master of Magic. But my favorite part of those games was just building a single army or two and just wiping the floor with the enemy. Well in HoMM2, you are encouraged to do just that very thing. Get a hero (or a few heroes) and focus on building up a huge army for him to battle the enemy. It's just so well executed on this simple premise. It has several expansions. It's only obscure because of age and being from the PC.
Katamari Damacy - This has several sequels, but few people know that the first game is easily the best. It has the best levels and the best music and the least crap that weighs down the other games. This game is short, but I've replayed it a ton of times. The sequel, We <3 Katamari, is also pretty good.
Theatrhythm Final Fantasy - This and the sequel are extremely addictive games for me. I really love Final Fantasy music much more than the music from any other franchise. This turns all of that music into a rhythm game. This is the sort of game that I will probably be playing for the rest of my life.
Mr. Do - This is an old arcade game that plays a lot like Dig Dug (another game I totally love.) You do a lot of digging but you also try to crush monsters by pushing apples on them. I highly recommend both this and Dig Dug to anyone who has never played either. (Optimally you will play them on an arcade cabinet.)
Anteater - I recently found this really old game at a nearby arcade. I can just play this over and over again for hours. It's a maze game, but you just run your tongue through the whole maze eating ants and worms and stuff. I like it more than Pac Man, but few have heard of it. It's so simple but addictive.