Thanks a ton for the response Rudi! This is exactly the kind of information I was looking for. Some of the terminology is a little over my head, which I more of less expected, but it should be easy enough to look up. I really appreciate you taking the time to lay this out for me.
You're right that examples can be a big help. One person's notion of the "definitive" songs of a genre can often be very different from another's, so here's a few of mine:
-Surf-
Misirlou - Dick Dale (Or pretty much anything by Dick Dale and His Del-Tones, really. His cover of Riders In the Sky is amazing.)
Pipeline - The Chantays (Hard to say whether I prefer the original or The Ventures' cover)
Mr. Moto - The Bel-Airs
Phantom on Lane 12 - The Mono Men
Daikaiju Die! - Daikaju
Even some punk songs have distinctively surf-sounding elements, like Agent Orange's Bloodstains or the Dead Kennedys' Holiday in Cambodia. Of course, a lot of Dead Kennedys' songs sound like really pissed off surf music, and Agent Orange has been known to do some freaking awesome surf covers.
(Just as a warning, those Dead Kennedys tracks are suuuper NSFW, and more than a little political.)
-Swing-
When I think of swing music, the first thing that comes to mind is Minnie the Moocher by Cab Calloway. Cab's pretty much the god of swing as far as I'm concerned, but just for the sake of variety:
Sing Sing Sing (With A Swing) - Benny Goodman
Is You Is Or Is You Ain't (My Baby) - Louis Jordan
St. James Infirmary - Louis Armstrong
Save My Soul - Big Bad Voodoo Daddy
Zoot Suit Riot - Cherry Poppin' Daddies
Hey Pachuco! - Royal Crown Revue
Stray Cat Strut - Stray Cats (Some might say this is closer to Rockabilly, but just listen to that bassline!)
...and of course, I'd be remiss if I didn't mention: Why Don't You Do Right? - Amy Irving (Sorry Peggy Lee, but you've got nothing on this version.)
Well, now that I've let my inner music nerd flail all over the place, hopefully that'll provide a better cross section of the kind of musical styles I'm referring to.