Crowning Music of Awesome: Any time he does his Neil Young impersonation. He even got the real David Crosby and Graham Nash to perform with him! And then there's his rendition of "Whip My Hair" with Bruce Springsteen...
History of Rap parts 1 & 2 with assistance from The Roots and Justin Timberlake
Hilarious in Hindsight: The Family Guy episode "Don't Make Me Over" depicted Jimmy Fallon as the host of a fictitious episode of SNL with the Griffin family (featuring a made-over Meg) as the musical guest (and Peter beating up Fallon for cracking up on-camera since only Caroll Burnett has earned the right to do that, not realizing that Fallon had sex with Meg as part of the show's cold opening). Why is this Hilarious in Hindsight? Because Jimmy Fallon actually came back to host SNL for a Christmas episode in the show's 37th season. The musical guest, however, wasn't The Griffin family or even Seth MacFarlane. It was Michael Buble.
The 1998 (season 24) Christmas episode hosted by Alec Baldwin [1] had a It's a Wonderful Life-meets-A Christmas Carol-style story that shows what the future will be like if Alec Baldwin phones in his performance on this episode. The episode predicted that in 2011, Fallon would come back to host SNL. It came true (only the date they gave in the 1998 episode was inaccurate, as December 12th, 2011 did not fall on a Saturday).
Just Here for Godzilla: With The Roots as his backup band people who don't like his comedy claim they only watch his show to see them.
The Scrappy: On SNL, particulary during the show's 28th and 29th seasons, when he gained notoriety for cracking up during his sketches.