You (and we) will need more information. You have the information in front of you, so it'll be easier for you to do this.
.db files could be from MSAccess, though if you're on a Linux system that would mean it probably wasn't an Access file.
Corel Paradox also saves .db files, as do many mobile devices. It could be an encrypted database file, in which case have fun.
You may try opening the file using any of the previously mentioned programs, preferably making a backup copy of the file first (obviously). You may also try opening the files with the SQLite Manager (http://www.sqlabs.com/sqlitemanager.php). I've used the SQLite for dealing with issues with iOS issues, but it's supposed to work with any sqlite databases.