Although it's a bit of an "ensemble" number and other characters interject, I really think a smart revision/rearrangement of Martin Short's "I'm Dying" (the Richard III number) from The Goodbye Girl could be great fun. "A Beat Behind" can also capture something similar for someone who's more of a dancer.
Martin also had a lovely 11 o'clock number, "I Think I Can Play This Part," that is a quite charming use of acting/theatre language to convey a lovely not-necessarily-romantic message of solidarity that's fun to ham it up to (but you can still be sincere). I have used that a few times at auditions for some "self-aware" characters with a heart of gold.
Great question, I'm sure there will be a ton more interesting answers!
Thanks to those who have responded so far. I expected a lot of interesting responses as greensgreens suggested, but think this thread got lost in all the Rent hoopla! ;P
The MOST meta of all meta songs has to be THE SONG THAT GOES LIKE THIS from SPAMALOT.
I would also include WITH ONE LOOK from SUNSET BLVD
There are entire shows that are built on a Meta foundation: SPAMALOT, BOOK OF MORMON and SOMETHING ROTTEN all constantly comment on themselves and the conventions of Broadway and actors. I happen to love MORMON, get a kick out of SPAMALOT...and, well, there's SOMETHING ROTTEN.
There are several from Ruthless.... "I Hate Musicals," "Born to Entertain," "To Play This Part," "Where Tina Gets It From," etc. You could make an argument that pretty much every song in that show fits your category.
ETA that "A Way Back to Then" from [title of show] is a great solo in this category. (Though of course all of [title of show] fits.)
There's a Cabaret song called "A Contemporary Musical Theatre Song" that pokes fun at the music of Jason Robert Brown, Kitt & Yorkey, and Joe Iconis that's pretty fun.
Everybody Wants to do a Musical - Nick & Nora Twenty Million People and Larger Than Life - My Favorite Year Backstage Babble and She's No Longer a Gypsy - Applause Intermission Talk - Me and Juliet Babette - On the Twentieth Century We Open in Venice - Kiss Me, Kate I Know What's Gonna Happen, What She's Doing, Unstoppable and The Most Important Night - Tootsie The Alto's Lament by Marcy Heisler (popular cabaret solo)
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian