I use LastPass, because it has add-ons for multiple browsers, plus an iPhone app.
I used to use Password Safe (free) but when I got a Mac I started looking into other alternatives. Password Safe is venerable, open-source, and there are compatible programs available for OSX and Linux. But you are on your own syncing across machines, and it doesn't have any real browser integration.
KeePass seemed most similar to PassWord Safe, but more up-to-date and with more features and third-party support. But I found it even more clunky than Password Safe (which clunkiness I was willing to put up with due to it's straight-forward simplicity), and wanted something with browser integration. Plus it really doesn't have great implementations on OSX and Linux.
I resisted the idea of storing this data "in the cloud", but am satisfied that LastPass does encryption locally and they do give you a local file that it uses as a backup source if the online service is unavailable (or if the company fails...). I haven't had any problems with sync, and use it across my Kubuntu box, MacBook, and Windows 7 VMs on both machines, as well as my iPhone.