I've been listening to the Bastion soundtrack recently and it's reminded me how rare it is to find video game soundtracks with distinct vocals (as in, no generic prerecorded "oohs" and "ahhs"). Obviously it makes some sense to avoid vocals in most soundtracks in general, so generally they're only used in end themes. Anyway, here are my favorite seven instances of songs in video games with distinct lyrics, not counting games with licensed tracks (like racing games and Alan Wake).
All of these are great and you should stop what you are doing and listen to all of them.
Bastion - Setting Sail, Coming Home
Journey - I Was Born for This
Portal - Still Alive (spoilers)
Portal 2 - The National - Exile, Vilify*
Skyrim - Dragonborn
The 7th Guest - The Fat Man - Skeletons in my Closet
The Curse of Monkey Island - A Pirate I Was Meant to Be
* I didn't actually find this song in-game; apparently it's like an Easter Egg?
A Pirate I Was Meant to Be gets tons of bonus points for being a song that is actually part of the storyline, as one of the most awe-inspiringly awesome unexpected moments of a video game ever.