during live shows handsome furs has played an array or songs, original furs songs, wolf parade songs, and covers of other bands. the ones i know from reading reviews of shows are:

Wolf Parade Songs:
Modern World
Same Ghost Every Night
Shine A Light

Covers:
State Trooper a Bruce Springsteen song
The Other Side Of Mt. Heart Attack which is a Liars song

Furs Songs:
Dumb Animals - there is a demo of this floating around and Wolf Parade has played it live
Hearts Of Iron - there are two demos, one from Inland Empire Touring and other one that I have no clue where it came from
Handsome Furs Hate This City - this is currently being streamed on their myspace
also these seven songs have showed up on Last.Fm:
Snakes On the Ladder
What We Had
The Radio's Hot Sun
Sing! Captain
Cannot Get, Started
Dead + Rural
Life Is Long