Well, yes, when listening to pop and rock music, it can seem like much of the vocal harmonisation moves in parallel motion (often in thirds and sixths), but there are plenty of examples of different motion out there, if you listen out for them.
I've always thought that The Beatles used some subtly interesting vocal harmonies. Below are the first 8 bars of the vocal parts from Love Me Do, their first hit from, ummm, I think 1962.
As you can see, just in the first 8 bars, there is a variety of movement between the parts. What I also find interesting is the amount of "bare" fifths between the vocal parts too; often parts are harmonised in "richer" sounding thirds and sixths. Along with the prominent harmonica part, this gives the song an earthy, folky sound. There are loads of analyses of Beatles songs, but this one reinforces and expands my thoughts.
The important point to be gained from this though, is that there are plenty of examples out there, if we take the time to listen to exactly what is happening in the music. And, maybe more importantly, when creating vocal harmonies ourselves, there is plenty of scope for experimentation.
(Apologies for the hastily cobbled together transcription, I think it's pretty accurate…)