FogBugz does the screenshot thing you are asking for. I have used FogBugz at my day job for years now. While it has it's quirks it is pretty nice.
UPDATE: OK, I can only find the screenshot tool [1] which is a downloadable desktop application as opposed to something I can integrate into my web application unfortunately.
[1] http://www.fogcreek.com/FogBugz/docs/70/topics/basics/Captur...