If only email is available then the users don't seem to engage.
A feedback box within the app feels like a step in the right direction, but doesn't offer any ability to build community.
Uservoice and tenderapp both look like they could work well, and GetSatisfaction seems like a better option once your app is in past the beta stage.
Things like Uservoice are great for generic suggestions and even finding bugs but they rarely answer your specific questions/concerns because that's not what they're there to do.
I also don't think they're that good at keeping a community together. Seriously. Pushing your users to another site where they have limited interest isn't in my handbook for cultivating communities.
You want:
... to keep users on your site. Pop-in JS things are okay if branded well. But they might still have to log in and then there's the problem of...
... to keep them involved in problems they raise. If somebody raises feedback, raise some back at them. Trap them in the process. Ask them more questions about what they feel is right or why they feel something was wrong in the first place.
... to make giving feedback desirable. One of the reasons SO works so well is its points system. Points mean prizes (or status and power, here) and that's a great way to make people want to keep going at it. Some users will just care and incentives just sweeten the deal but most users won't really care enough without the prospect of benefiting from it some how.
Just to skip back to the point that external services are too generic for directed feedback. As a developer, you sometimes need to ask specific questions to know when something needs changing and this feedback usually needs to be asked at very specific points, usually after a task.
Stick feedback questions on your site at the end of tasks. Eg if a user posts a new something-or-other, at the end of the process, stick an unmissable box in there, asking them how it was for them. You can ask relevant questions and you'll catch more problems because people have just done the task (opposed to them noticing your feedback tab 10 minutes later when they've forgotten half of it).