Some of my favourites:
Arlo Guthrie: City of New Orleans
Looking Glass: Brandy (You’re a Fine Girl)
Bobby Darin: Mack the Knife
Gene McDaniels: A Hundred Pounds of Clay
Charlie Daniels: Devil Went Down to Georgia
Jerry Jeff Walker: Mr. Bojangles
Elton John: Candle in the Wind
There are others, but these are the ones I always look for. Sometimes, just for fun, I’ll also do a couple of “talking” ones, doing the necessary voices:
C.W. McCall: Convoy
Ray Stevens: The Streak
I sometimes get standing O’s for my “Delilah.” Other than that, the crowdpleasers in my repetoire are “Secret Love,” “Unchained Melody,” and “Angel from Montgomery.”
leafrog if your Hill o’ Clyde is near Seattle, the Crescent on Capitol Hill has a decent sized book. I think they do karaoke most if not every night. Mostly gay clientele, lots of fun. I don’t know about their showtune selection but I know they have a good selection in general. (I’ve only ever sung there and the Bus Stop.)
In a wonderful comedy of errors, the only time I’ve karaeoked in public was at a charity event that included a beer garden. By the time I got my nerve up, everyone had spend large amounts of time in the beer garden taking in large amounts of beer, and the karaeoke mic had died between my turn and the person before me. I got up and did what is now remembered as a kick-ass version of “Breaking Up Is Hard To Do.” Actually, nobody remembers that they couldn’t hear me because fo the dead mic, and I get feel-good points for shelling out for charity for the opportunity to make a damn fool of myself. Kindof a win-win for everyone!
If I ever get roped into it again, here are some songs I could picture myself attempting:
Lights - Journey
Winner Take All - Styx
Hollyann - Boston
Mystic Rhythms - Rush
Chiquitita (sp?) or Fernando by Abba
Cocaine Blues - Johnny Cash
Jackson - Johnny and June Carter Cash (if I could find a willing male to sing with me)
When He’s Not Around or In Blue - The Corrs
Orinoco Flow - Enya
This Is Why I Say Goodbye - Podstar - a now-defunct local band - doubtful if it could be found on any karaeoke list, but I know the lead singer and it’s a great song that I can actually sing. Some of them are now part of Dead Girls Ruin Everything, for those in the KC/Lawrence area.
I’ve only done karaoke a couple of times, but my best experience by far was with Icehouse’s Electric Blue. I don’t know why, but it’s pretty much perfect for karaoke, and I’m definitely singing it again if I get the chance.
I learned a few Japanese songs back in my bar-hopping days in the sticks, since inevitably someone would push a microphone on me, and while singing an English song would be a bunch of incomprehensible off-key babble, singing in Japanese would be met positively regardless of how badly I carried a tune.
In English, I’ve learned that Elvis is always safe, while Cheap Trick is deceptively hard to do well.
When I do go out for karaoke with people I don’t mind annoying, I’ll do Jethro Tull’s Locomotive Breath and anything by David Bowie.
I only do Sinatra. Badly. Well, maybe better than most. I’m definitely a crooner. 
Most of my favorites are not commonly found on the karaoke lists. The only popular tunes I fancy which I ever find on Sinatra karaoke lists are: Witchcraft, Nice & Easy, One For My Baby, My Way
Everybody gets tired of hearing those though. I know the man had quite a body of work, but why is it so hard to find Sinatra karaoke that hasn’t been heard a million times? Y’know, some swingy, upbeat stuff that’s just plain fun to sing and puts people in a good mood instead of depressing the shit out of them.
An abbreviated list of “hard-to-find-on-karaoke-list” Sinatra favorites: American Beauty Rose, Come Dance With Me, They Can’t Take That Away From Me, Oh Look At Me Now, Something’s Gotta Give, The Way You Look Tonight, Young At Heart