Unexpected positive experiences eh?
Well, if you talk about unexpected, the first and most recent I can think of is FFVII:Crisis Core. I had not really had any big hopes for the game since I'm not the biggest fan of FFVII, but I thought that Crisis Core was quite a decent game after all. The fighting system had it flaws and could have been better, but somehow I didn't get bored by it. It was different from anything else that I'd played, so I guess that's why it kept my interest. The story had a boring start, but in the end it turned quite good IMO. I kind of like how the main character matured, and I really wanted to know how it all would turn out. A rather short game, but it was a nice break from other games.
Another one I can think of was Earthbound (although that was a much much more positive experience :P). I remember starting up the ROM at the computer at home and the title screen came up, "Earthbound, the battle with Giygas" (if I remember that right). I thought, man this game looks like crap at the first glance since the title screen was all but pretty. I was wrong. When I got my first look over Onett, I just knew it wouldn't be my last
Playing the first Mega Man Battle Network game. I didn't quite know what to expect when I started the game, but it turned that the concept was cool with running around in the cyber world and what have you, and the battle system was THE AWESOME. I loved the mix of action and strategy in the game and the addicting gameplay truly made me crave for more, so I played the second and third and they were just as good, the third being even better than the other two. The Battle Network games are truly underrated I have to say (well, at least the games up to the third are good, I haven't played the others but I've heard they're not as good), and I'd say that most people who say they don't like it haven't given the time needed to learn the system (which can take quite a while).
Buying Grandia II for the PC was just by chance. I was at the game store and saw the game in the bargain bin, I knew I had heard the name before but knew nothing more. So I bought it since it was a RPG and that the cover was kinda cool

That game has one of the best battle systems I know of. I can't think of many games with as good battle systems like this one. Great game.
That's all I can remember right now, I'll think on it for a while and see if I can come up with something else.
Jam it back in, in the dark.