I remember writing two or three poems, but I don't usually read poetry. I'm more interested in non-fiction and sometimes also fiction books. However, if they're cleverly made, I may enjoy poems very much and remember them for a long time. And I'm impressed by works like Goethe's Faust which are almost completely told in rhymes.

If it's a story (like in Faust) then I'd read it from front to back. But if it's just a collection of poems I wouldn't mind skimming through the book and reading whatever attracts my attention.