The Kindle and Nook iOS apps both let you copy/paste. I did it all the time when I got stuck having to use DRM ebooks in school, and never had a problem with it. There may be limitations on how big a region you're allowed to do it with, but, if so, the limit's large enough that I didn't encounter it in the course of normal academic use.

I did sometimes run across ebooks that basically used images of the text instead of actual text, and copy/pasting from those naturally doesn't work. But the ebooks in question were all non-DRM.