Assuming the word "contemporary" was perhaps not intended, I would say Sonata form is the most common, and variations on that form.
I've always wanted to know a bit more about form and structure--I have been through the standard theory classes (and then some) to get a music degree, but that stuff gets quickly lost if you're not steeped in it, and no matter how much I go back to the old books or explore some newer things, my brain just doesn't retain the info. When I listen to works nowadays, I really don't hear "structure" when I listen, I just hear the music, and only when I encounter things after a few listens (or plays) that I believe weaken a piece do I start to think about what structure it is.
When I study scores, though, I do attempt to label themes, key areas and large portions, but I don't get detailed.
It seems frequently when I read about music of the 20th century, writers attempt to squeeze everything they hear into the standard forms as much as possible and make a point of saying how a piece is in a "modified Sonata form" or something to that degree, even if the relationship is very tenuous.
