I'm biased here, but I think the two teams that got the most out of their draft packs were Chicago and Philly.
Chicago got a proven Pro Bowl quarterback, which already makes the draft a winner. I like a bunch of their other picks, too (Gilbert, Iglesias, Moore, and Freeman, most of all) but this is all about Cutler.
The Eagles had a great draft, both in terms of veterans and draft picks. Maclin and McCoy were great choices, and the trades for Peters and Hobbs were excellent, as well.