I always get an enthusiastic response when I do “The Devil Went Down to Georgia” but substitute . . . the other lyrics. 
Me and a buddy used to do Titties and Beer. I’d do the devil and he’d do Frank. I’ve also sung War Pigs.
I love the karaoke room at cons. I remember the year that a friend and I brought down the house with our rendition of “It’s Raining Men.” The following year I was cosplaying Porrim Maryam, a Homestuck character who, shall we say, has been in a lot of short-term relationships. Of course, I just had to sing “Like A Virgin.” 
In a horribly inebriated state I sang Paradise By The Dashboard Light with a woman I didn’t even know. And we were good, I’ve been told.
My mid-90s employer always brought in a karaoke setup for the annual company summer picnic. There was a contest among departments, complete with costumes, and since the picnics always included alcohol, the karaoke got pretty hilarious. One year my department did Warren Zevon’s “Excitable Boy”. We had a lead singer who was actually pretty good and could do the Zevon voice mannerisms impeccably. I, along with two male co-workers, made up the backup ‘girls’ (ooooo wah oooooo, oooo, ooo, excitable boy). The guys were in drag. It was tremendous fun and we got the prize!
"It’s Raining Men in a packed sports bar.
(The only reason that’s interesting or amusing is that I’m a 250 lb, bearded hetero and I took great pleasure in making the meatheads uncomfortable.)
“Sylvia’s Mother” by Dr. Hook
The bar across the street from my longtime employer was a gay bar. It had a fabulous happy hour/karaoke combo on Wednesdays.
Anyway, one Wednesday, someone talked me into doing karaoke. I chose “Where Did Our Love Go?” and proceeded to get into it. After the first stanza, four cute guys came onstage and did pefectly-synched background dancing. It was hilarious!
I figure the older and more obscure songs give me a better chance at sounding ok, since everyone doesn’t remember every single note they might not notice if I’m a bit off here and there. So the hokey song I do is Harper Valley PTA.
Hot Diggity Dog (Ziggity Boom), as performed by Perry Como.
When she was seven, my little girl used to love that.
I am told that once, with the lubrication provided by many rum drinks, I once channeled Vickie Lawrence quite notably on “The Night The Lights Went Out In Georgia.”
For sheer unabashed cheese, it’s hard to beat On the Wings of Love by Jeffrey Osborne.
I once tried ‘Stairway to Heaven’ - the vocals are good, but they’re so out-weighed by instrumentation that the karaoke bloke ended up fast-forwarding through much of it, which rather spoiled the moment.
Another time, while bitter over a recent break-up, I did a foul-mouthed version of ‘The Lady is a Tramp’, which the crowd loved. The pub-owner was less impressed, and I was barred for two years.
“Paradise by the Dashboard Light” as a duet with any girl (typically a good friend, obvs) who knows the words, can sing it, and doesn’t mind getting groped for a laugh.
Minnie the Moocher.
I do an excellent a capella Mercedes Benz by Janis Joplin. Best thing is I don’t even need to make sure the music is on the machine.
Please keep in mind, though, that the thing is almost 9 minutes long and is basically a medley of three songs (plus a baseball commentary). It’s best performed in a private room setting, or on a very slow night at a bar. In a place with a long rotation going, it can be inconsiderate to take two or three times as long as everyone else.
And don’t get me started on people who try to do American Pie without any idea how the verses go.
I’m a complete karaoke nerd, by the way.
I have been told that one ST. Patrick’s Day I sang “Danny Boy” in a local Irish bar. I have no recollection of it, and if any of you were there, I offer my apologies.
I have what is likely to be the worst singing voice in the world. Imagine Dennis Hopper doing a vocal impression of Stevie Nicks…
I sing “Minnie the Moocher” as well. It is one of my favorites to sing when I go out and do karaoke.
The funniest that I have sung are the following:
“One More Minute” by Wierd Al. It always gets a laugh.
The Masochism Tango" by Tom Lehrer.
My favorite of late that is not a comedy song, but I turn it into one. I sing “Shotgun Blues” as sung by the Blue Brothers. During the guitar solo, I recite a short monologue of Rodney Dangerfield one-liners that makes the crowd roar.