First time, through? Not many.
I usually go back through games for speed-runs and other such nonsense.
Here's a few easy ones: Portal, Trine, Braid (though the speedrun wasn't easy), Mirror's Edge, Zombie Driver, Raiden 3, pretty much any fighting game "story mode," UT, Q3A, Doom, Doom2, Duke3D.
Here's a few I'm actually more "proud" of.
Ocarina of Time- Took a while, but it was like the 4th or 5th time I finished the game. I didn't get 100% on this save - there's too many tiny things that you can only do as a kid or before certain things happen that I didn't bother trying to do in this save (beanstalks, etc.)
Starfox 64 - Doesn't sound hard, but I had recently gotten a new cartridge so I had to get all the medals, then beat it on hard, and get all the medals after I unlocked hard-mode too. Which takes at least 6 playthroughs to go to each level, assuming you get the medal the first time - I think in total it took 11 or 12 playthroughs each taking a different route.
Hammerfight - This game isn't exactly easy, but it was very engrossing to me, and I finished the story-mode on the day I started playing it. I started a second play-through to make different choices but never finished that one. I ended up just taking my first play-through and putting it through the Arena matches.
