Sure you have. More specifically, you become aware of a line or two that makes you think, "Hmmm, I'll bet the writer only used that word right there because it rhymed." For example, you might hear something like:
"Oh, she was his one desire, the one who took him higher..."
A line like that, aside from being cliched and sort of banal, is one of those lines that the author probably used because it was an easy rhyme and it "fit." Sometimes writers reach for easy rhymes because they want something simple and accessible to sing, but that's a fine line to walk because if you're not saying anything at least semi-interesting, you're also flirting with being forgettable. (Have you ever tried to memorize a song made up of a bunch of strung-together cliches? It ain't that easy.)
The desired goal, at least when it comes to pop songs, is to balance the familiar, simple and common with the unique, clever and compelling. Not so easy when you think about it! So rather than immediately settling on the first words that "fit," see if you can come up with a rhyme that actually expresses what you want to say. But be careful; you don't want to replace a cliche with something that sounds forced, awkward, hokey or contrived. The ley is to actually say something intriguing while STILL being relatively straight forward and catchy. In other words, you wouldn't want to change the line to something like:
"Oh, she was his one desire, got him caught in a love quagmire..."
just because you're trying to be "clever." That lyric just plain sucks, in more ways then one. However, you COULD try to change the initial lyric to something like:
"Oh, she was his one desire, another object to acquire..."
The words are still ordinary, everyday words, but "object" and "acquire" are used a little less frequently in pop music, and have a little extra panache. However, they still sound like something someone might actually say off the top of their head. Not only that, but now the lyric is telling us something. With just those few simple words, the listener can start getting all sorts of mental images of these characters. (The guy sounds like a douche, to me.)
This is not to say you can't play around with more exotic rhymes. It all depends on songwriting context or what sort of "feel" you're going for. Just be aware that what sounds fanciful and clever in one setting can sound awfully stodgy and stilted in another. For example, if you're going for a more literate, broadway-influenced feel, you could try something along the lines of:
"Oh, she was his one desire, with roses and candy he plied her..."
but, in general, you'll want to stay away from language like "plied her" if you're writing, say, top 40 dance tunes.
I also don't mean to suggest that you can never develop a unique "voice" or use stream-of-consciousness imagery. In fact - and we should get this out of the way right now - there are ALWAYS goung to be exceptions to the "rules," but unless you're a super-genius like Mozart, it's probably a good to get an idea of what tends to work and what doesn't. It's because there IS a logic to strong songwriting that the brilliant exceptions work so well.
So take this as a general rule of thunb: Don't quickly settle on the first rhyme that pops into your head, just because it's easy and obvious. It can come across as kind of weak, and even worse, it can draw attention to itself and pull the listener out of the song. Try coming up with something equally straightforward but a little closer to what you're trying to express (and if you don't yet know WHAT you're trying to express, that's a whole 'nother issue for a whole 'nother post).
Besides, you can always go back to your original rhyme if you feel that it truly captures the thought or the passion and immediacy you were looking for. Heck, there have been many times that I've gone with a working lyric or two because the rewrites didn't quite fit the mood. Just don't be sloppy or lazy about it, because lots of lyrics you think were just "tossed off" someone's head were actually painstakingly refined for maxiumum effectiveness.
Now get back to driving. You wanna get in an accident or something? Sheeesh.