Random Topic - Distinct Songs

Circumstances have arisen whereby I feel like I am having the same conversation with vastly different people on a regular basis. The conversation basically goes like this: Person A says, "I like Song A because it is different from just about any other song out there, even from other songs by Group A (singers of Song A)." Person B replies, "That is a great point, I also like Song B for the same reason." This inevitably leads to Person C (me in many cases) pondering aloud, "I wonder what OTHER songs there are like that?" Now, the criteria for which songs merit inclusion in this "conversation" seem to shift: for some it is a song with a distinctly different sound than the artist's other works (Group 1), songs with distinct "breaks" or sound changes within the song (Group 2), and songs that persons who might not like any other song by the artist would like that song (Group 3).

I now offer examples of each Group from different types of artists:

Group 1

"Vox" by Sarah McLachlan
"Amen Kind of Love" by Daryl Singletary (I'm partial to this as it's my wedding song, so be nice)
"Fast Cars and Freedom" by Rascal Flatts -- thanks to Velvet for this one
"Everything Will Be Alright" by The Killers

Group 2

"Politik" by Coldplay
"Port of Amsterdam" by David Bowie
"Bad" by U2

Group 3

"New York, New York" by Ryan Adams [sometimes "Rescue Blues" as well]
"Friday Night Lights OST" by Explosions in the Sky
"You'll Think of Me" by Keith Urban

These are just some examples that have been bandied about... please feel free to add or disagree (preference for the former over the latter), but help me to be better prepared for the next time I have this "conversation," presumably tonight.