They Might Be Giants are famous for this. Among others, you have:
“and now this song is over now, this song is over now”
“It’s a brand new record, for 1990: They Might Be Giants’ brand new album Flooooood!”
“Make a hole with the gun perpendicular to the name of this town on a desktop globe: exit wound through a foreign nation, showing the home of the one this was written for,” and later in the same song:
“Everything sticks like a broken record - everything sticks like a broken record - everything sticks until it goes away…”
“I like to play the drums; I think I’m getting good but I can handle criticism. I’ll show you what I know and you can tell me if you think I’m getting better on the drums…” (while the drummer goes from a clever light beat to an aggressive caveman bashing)
And in their perfect pop/techno song Man It’s So Loud In Here, they use every single cliché ever used in dance music including some of the best drum machine programming ever, and sing “Baby, check this out, I’ve got something to say – Man, it’s so loud in here! – when they stop the drum machine and I can think again, I’ll remember what it was.”
Mark Knopfler sings about not wanting to make a guitar “cry or sing” in Sultans of Swing, but then proceeds to do exactly that in the spaces between lines – that whole song is practically a tutorial on how to be subtle and brilliant playing electric guitar in a rock song, but it’s disguised as a paian to a forgotten swing band.
And of course, I need to mention Alan Jackson for his Three Minute, Positive, Not-too-country, Up-tempo Love Song, which starts with the line “This is a three-minute song” and ends at 2:56 with a guitar note, held for four seconds as the singer talks to his producer:
“Hey Keith, how much time was that?”
“About 2:56.”
“We need four more seconds!” Guitar hit, and the song actually ends, precisely at 3:00.
…and, as much as I hate to admit it, rappers have been doing this for ages. “My name is (whoever) and I’m (whatever) and I have so much effing money and cars and (whatever)”. Yawn.