Definitely turn-based classics. As I've already posted elsewhere, "Laser Squad" on C-64 probably started my passion for APs, TUs and such. When I've finally got into PC gaming, "Jagged Alliance 2" instantly became - and remains - my beloved title, followed by "Silent Storms" and first "Fallouts". Yeah, I like first X-Coms too, but these are quite different from "JA2" in many aspects, so trying to determine which one is "better" is pointless to me. Let's just say I love them all.
"GTA 3" - first game I've modded. OK, "cool story, bro" time: that was back when "internet" was still quite a mystery to me and back where I live most people hadn't had any connection - including me. I know virtually nothing about coding, but when I was inspecting GTA game folder, I've discovered lots of ".dat" files. I only knew, that this was an extension of general data files, meaning that they could contain any kind of data - music, pictures, text... I've noticed, that they are small in size and so I've tried to open them with Notepad (later I did the same with various ".ini" files). What happened next was an orgy of tweaking: from car colors, to gang members stats, to pedestrian behavior. There's no funnier sight, than an angry grandma chasing down the street a group of scared and helpless cops, clubbing them with her purse... Or starting a fire and observing a squad of firefighters running scared from the flames
"Neverhood" - game that showed me, that games can be truly an art, and also can be witty and well-written. Later, I've noticed that some games have actually better writing and even better acting than many contemporary, high-budget hollywood movies. I think that's how I became a gamer - I love movies, but when the movie industry started to eat its own tail, well...it's time to move on. Personally I think it's true especially nowadays - movies are being made strictly with profit in mind, writing butchered to fit PG-13 rating (so more kids will buy tickets), overblown expositions and "spoonfeeding" are ubiquituous, so nobody has to use their brain while watching, one cliche is chasing another, "political correctness" nonsense kills even the best scripts... I could go on. That's why many people miss videotape era or classics from 90s. Original "Robocop" is not better "because nostalgia" or "oldschool". It simply IS better. For a long time video games provided me with the level of entertainment the movie industry couldn't reach anymore. Sadly, what happened to cinematography happens now also in videogame industry. Thank God there are still companies like CDProjekt (and I'm not saying that just because I'm from Poland), that can develop a game without trying to cater to "everyone".
Since I was comparing videogame and movie industry: "Privateer - The Darkening". Clive Owen ftw! God, I loved the idea of joining virtual worlds with real-life acting. Why was it even abandoned? Yeah, I know the answers... Still, games with actual movie actors were instantly ten times better than anything else, and at some point there was so many of them. "Command & Conquer" series wouldn't be half as glorious without real chicks... (and I was quite surprised seeing Jennifer Morrison in one of the games)
Last, but not least, the game that showed me the potential of sandboxes... No, not GTA... It was "Omikron - The Nomad Soul". Not "really" a sandbox, but playing that title I felt incredible freedom - probably because how well the game world was designed, and I'm not talking just about maps. I'm talking about the game mechanics, which allowed player to change the playable character "on the fly", about the world that really felt "alive" with its inhabitants, the whole artistic game concept. Plus David Bowie lending his face and voice for multiple game characters was also incredible. I often found myself hunting for in-game hints how to find and attend one of "illegal" music concerts, rather than focusing on actual plot.