I am trying to find an online database application that plays nicely with my BB and is cheap, or preferably free.

I've come across blist (requires flash), zoho (free version is only 3 databases), and quickbase.

Surely there has to be others. Anyone got one to recommend?

See if these help your situation.

Handbase DDH Software -
Inform : Mobility solutions for the individual, team, business and enterprise - Skysoft Systems

Yes, those would be nice if I was looking for an application on the device, but I was looking for something online that I could view and edit from both desktops and mobile devices without adding software.

maybe you can make a database in Mysql or something host it on your server and write a mini interface for it in html or something that you can access from the BB and you can access it from the Desktop aswell.