Pretty much Sin & Punishment back when I got it off of VC on Wii. I know well there are others, but I honestly don't remember; I have certainly beaten many games within the week that I've gotten them.
Other than that, I recall way back when I nearly beat Fighting Force the same day I rented it, but the last boss handed my ass to me.
- Aladdin (Game Gear)
Reading your comment jolted my memory into remembering that I beat Aladdin for the SNES the same day I rented it. Granted, I think I took a break or two and returned to the game using passwords, but I still finished it on the day I got it. I didn't get the special ending, though.
Some games are short enough to complete in single sittings though. I think it took me less time to 100% Megamind for the 360 than it did to watch the movie.
It's all about presentation.