Webapp only for the foreseeable future. The security/privacy is something we've spent a lot of time and effort on. (Our CTO is a crypto by trade with a focus on financial applications: http://www.eecs.harvard.edu/~cat/ ) Thanks!
Mint.com has millions of users who have provided that information. That said, in the medium to long term we're working on a unique solution that will permit you to keep your usernames and passwords only on your local computer while keeping the less sensitive data (transaction history, balances, etc.) on our servers.