If you have command line access to the server you can also connect to MySQL then run

show databases;

Though your control panel should also tell you the name and path of your database.

Run a CRON job if on Linux or Scheduled Job on Windows and backup the database and Website every day would be my recommendation.

I back mine up each day and then RAR them so the size is acceptable to me.

I have a monthly cron set to backup specific paths and ftp files to my local server...

For my SQL files I backup the raw SQL storage directories, for the time being anyhow

Well my next step will be to FTP the backups to another site on another server at least once a week just in case the hard drives fail or something on the main site, the most I could ever really loose is a week of posts. That is a worse case scenario.

If I had physical access I could hook a tape drive or external drive to the system - but since the site is about 8,000 miles away I don't think that will happen.

My setup is as follows:
1. Server creates backup according to specific directories i wish backed up; this is done to a temp directory.
2. ncftp is set to ftp all files to a remote host.
3. Remote host (my home development machine) sits and recieves files, very litle that i have to do, but I can backup files in house through the dvdrw drivves n the server (which works out fairly well)

I went through ncftp and customized my settings, and have everything issued through a cronjob, I could ajust the crontask to run however often as needed (should I be that anal retentive);

I could also take and setup a seperate task to do just the db or any other set of db's to account for forum data that i'd want backed up.

Everything ofcoarse is tarred before transferred over, i have it done by sites (from my VPS); I rather enjoy the level of customization that there is, always up to learn hehe

Well I just took over as Admin of the site a couple weeks ago after a loss of accounts and no backups.

Got the board back up and running, now have upgraded it, and back it up daily. So it's in much better shape then it was in the past. Had there been a bigger error or full data loss there was no backup period.

I have a similar issue with a friends site, the host made no backups, and neither did he; well the host migrated all of his sites to a new server and left my friends on the old one and the bill poped and the server data is magicaly gone; so now theres no hosting, no backups, etc and no one knows what happened...

Pretty scary :/... If we can get data backup I'm going to ensure weekly backups of the database, with monthly backups of the site.