Oh gosh, I have a bunch of video games I'm in the middle of my first playthrough of. I'll list them in order of most-recently-played to least-recently-played.
Super Mario RPG - I just started it about a week ago, and just got Mallow in the party and beat the first boss.
Legend of Zelda: A Link Between Worlds - I'm clearing the Dark World dungeons now, enjoying a combination of nostalgia (A Link to the Past was the first Zelda game I played) and innovative wall-traveling.
Kingdom Hearts - Just defeated Jafar; my party is around level 25. I'm playing the Final Mix version of this game, and it's currently the only PS3 game I have...
Legend of Zelda: Ocarina of Time - I'm trying to remove the barriers around Ganon's Tower, and every time I get enough Rupees, I head to Lon Lon Ranch for the millionteenth attempt at those stupid horse races.
Chrono Trigger - I'm at the point where the game lets me loose and I have to figure out which sidequests to do. Trying to level up some more for the final boss. Meanwhile, I'm recording video footage of the DS version for a possible future Let's Play (but have been playing the SNES version thus far).
Final Fantasy VI - I have, uh, just tried to overtake some sort of gate to Kefka's domain, by traveling through a cave full of zombies? Been quite a while since I last played and I can't remember what's been going on.
Banjo-Kazooie - I've really been enjoying this game so far, but it's been a long time since I last played. I think I stopped around that level with the giant metallic fish.
Kirby 64: The Crystal Shards - I've defeated Miracle Matter, but have been trying to find the remaining shards. It's being very difficult and I might need to consult the Internet soon.
Super Metroid - I recently defeated a boss, which I think is the first or second one... the levels flow together so much that I can't remember which level I'm on.
Conker's Bad Fur Day - I'm stuck on a level where you have to quickly throw knives at chains in a building with rising levels of electrified water.
Kirby's Epic Yarn, Okami, Super Mario 64, Donkey Kong Country 2 - It's been so long since I played these that I can't even remember where I left off.