I don't know what's going on with my server but periodically, the server CPU will spike and require a reboot.

I'm running Drupal 6 - which means PHP and mySQL. Postfix/Dovecot is also install, both via webmin.

I'm new to this VPS business, so any help would be appreciated.

Did you take a look at this thread ?
http://www.linode.com/forums/viewtopic.php?t=4283

Most of the time, CPU spikes like that are caused by having too many Apache processes/threads.

MySQL is also a memory hog but it usually won't exceed a certain limit, especially when you use the Debian/Ubuntu default config with the moderately low buffer settings. Apache, on the other hand, tends to get out of hand very easily in its default settings. You need to cut down on the number of processes/threads/max-clients or it will crash your server whenever there's a bit of traffic.

Even better solution:
http://www.lighttpd.net/
http://nginx.org/