Keeping MySQL up to date is easy to do with replication, if you can direct all of your database inserts and updates to one server. It gets a bit more complicated if you're concerned about security (which you should be).
http://www.mysql.com/doc/en/Replication.html
If both servers are in the same datacenter, and connected together directly through a second NIC card, security is not an issue. That link is guaranteed secure, since it's not on the public Internet.
If that's not the case, however, you need to look into stunnel, CIPE, PPTP or IPSec to secure the connection between the servers. MySQL 4.0 and higher also has SSL support built-in, but I've never used it, so I can't comment on it.
You could also consider using cron to do a scheduled mysqldump into a text file, transfer that file with scp or rsync, and then import it into the second server. That could get a bit messy, though.