What's with everyone picking games that are actually steady franchises/good games? I mean, what's the point of putting "Gears of War 2" as it's not really a pet game, it's just a good game you like. In any case, I have a bit of a three-way tie:
Killer 7- God I can't get enough of this game. Though I never play it anymore, because the real attraction is the story and once you get it, it loses it's playable charm, the game is still amazingly awesome in my eyes. Just the weirdness factor had me playing constantly. Though it doesn't have much wrong with it, people seem to really hate the fact the movement in the game is rail-shooter based, which I never had an issue with. Invisible enemies are another odd thing to put in, but it never turned me off. If you want a really wacky Japanese horror style game, look no further than Killer 7.
Blackthorne- Easily the only "flop" Blizzard has had, Superman not withstanding. I'm not sure why this game wasn't more popular, as it's really good. Part adventure game, part shooter, it's really just fun to run around with a shotgun and shoot at orcs and trolls. It even had a pretty innovative "cover" mechanic where if you hit the shoulder buttons on the SNES controller, you'd duck into the background and dodge gunfire, though not bombs. Really, just a well made game that never caught on.
Rage of Mages- This is probably the penultimate "pet" game of all time. Published by Monolith Studios and developed by a small dev team over in Russia, this game kicked ass! The RTS style camera to control your warriors and mages was just really neat and everything just felt super balanced. The progression was fairly deep in terms of character developement with each weapon/magic having to be leveled up through use and the equipment varied greatly. The best part is that you actually had to rely on your allies! Mages could fling spells with ease, yes, but they would be killed in two to three hits by anything mid to late game. Warriors, on the other hand, could trod in with heavy armour and health potions and survive most things, but because enemies quickly develope resistances to most physical weapons, their damage output tends to be poorer for it. This meant that you had to tactically find ways to position your party to defeat any sort of large monster in order to progress. Truly a masterpiece of gaming if I ever saw one. =)