When I think of my favorite acoustic version of a song, the first thing that comes to mind is Everlong by Foo Fighters.
I like hearing alternate versions of songs that are loud and/or fast or involve a lot of different instruments and seeing how they work in a (often times) slower melody with a single instrument. I dislike when the song is changed for the sake of an acoustic version.(example, Placebo - Every You and Every Me)
Some other favorites~
Alkaline Trio - Every Thug Needs a Lady - My favorite Alkaline Trio acoustic version of any song.
Alkaline Trio - Emma - A perfect example of how Matt and Dan's harmony works so well together.
Alkaline Trio - Private Eye - "this song's for Dexter"
Brand New - The Quiet Things That No One Ever Knows - aaaah I melted when I first heard this
Metric - Help, I'm Alive - completely haunting.
Panic! At the Disco - Lying - I love acoustic Panic! songs because they show just how amazing Brendon Urie's natural voice is.
Panic! At the Disco - I Write Sins Not Tragedies
Panic! At the Disco - Nine in the Afternoon
Shiny Toy Guns - You Are The One - The whistling freaked me out at first, but they came through.
Yeah Yeah Yeahs - Maps - A regular fixture for my acoustic playlists.