I use Keepass.

My database is stored in a DropBox directory. Because I don't fully trust Dropbox, Keepass is configured to use both a password AND a keyfile (which is NOT stored on dropbox)

That covers my "normal" system use case - both the database and the keyfile exist on my normal machines. If I'm setting up a new machine, DropBox will bring in my Keepass database, and I manually copy in the keyfile either from another system, or from a USB key.

My phone (Nokia) doesn't support either DropBox or the current format of Keepass, so it's a manual process to export the database to it occasionally, and hope I don't need anything else in the interim...

If I really need to access it on another computer such as a Coffee Shop I can (via DropBox website), but unless it was an absolute emergency I wouldn't - there's just too much chance of keyloggers and the like which could steal the entire database and the password.