I'm only 13 years old. First non-shovelware game I can remember playing was World of Warcraft. Does that make you feel old?
Might & Magic III - VI: I always was a huge fan of HoMM III but I didn't know what to expect. Wow, they are fantastic games. Combat is mediocre but everything else more than makes up for it.
Thief II - After three games people claimed were awesome but I hated (Deus Ex, Morrowind, SMAC), I was very nervous about Thief II. Just to make it worse, I am very impatient and HATE old stealth games. Thief II surprised me. I was having a ton of fun, because the game gives you options and understands YOU ARE NOT STUPID, without becoming the extremely frustrating "One pixel out of cover and you get bullshit detected" nonsense. Also I enjoyed getting lost in the level and picking up everything, and then reading the notes. And the story is fantastic. It's not sunshines, lollipops, rainbows, and a superhero main character. NO. This is a dark and gritty story and Garrett is just a man trying to steal, not save everyone. Wow.
Fallout - I got this for free, and I wasn't expecting much because most people who LOVE Fallout 1 HATE Fallout 3/NV. I liked Fallout 3 because of the atmosphere (NV did better gameplay). The atmosphere here is even better, the jokes are great, and the gameplay isn't too bad either.
Baldur's Gate II - My dad played this in university a bit too much (Never beat it though), and everything he says about the game made me purchase it. I never thought I could be so immersed into a game's story. It's just so great. The gameplay feels a bit odd though, and it gets annoying being attacked by murderers every 30 steps in the city. I play it about once every 1-2 weeks.