This could work by encrypting your database in a truecrypt volume that must be mounted by entering the password. Thus, the data is only ever saved on disk in encrypted form, and the key to access the data is not saved on the disk. Of course, it is still in principle possible for anyone to access that information if they have physical access to the computer while it's running, but at least this makes that much harder.
It's not feasible to run databases on encrypted block devices. Some databases let you encrypt certain tables or columns, though.
for example, my laptop disk's main partition is encrypted. i need to enter the password when i boot, but nothing terrible happens if i lose power or the system crashes or whatever.