(Copied over from an article I just put on Stack Overflow)
The folks at MSSQLTips have some very helpful articles, the one most relevant for this is "Automating SQL Server 2005 Express Backups and Deletion of Older Backup Files"
The basic approach is to set up two tasks using the Windows Task Scheduler. One task runs a TSQL script that generates separate backup files for all MSSQL databases (except TEMPDB) with the database name and a date/time stamp in the file name into a specified directory. The second task runs a VBScript script that goes through that directory and deletes all files with a .BAK extension that are more than 3 days old.
Both scripts require minor editing for your environment (paths, how long to keep those database dumps) but are very close to drop-in-and-run.
Note that there are possible security implications if you're sloppy with these or with directory permissions, since they are plain text files that will need to run with some level of privilege. Don't be sloppy.
I don't know about the requirements for master/slave type setups with MSSQL, but it does support replication and there's documentation out there. Hopefully that same documentation will indicate whether it's possible to do it with MSDE/Express as well as with the full product.
Original answer, revised to down here because my reading comprehension was poor and I read MSSQL as MySQL:
For database backups, look at the MySQL documentation. Among other options, mysqldump or (possibly) mysqlhotcopy will let you dump the contents of the database for backup even while it's in use. From my reading of the documentation, you'd generally not have noticeable interruptions.
One drawback of this approach is that it gives you a new dump file each time, so rsync may not help cut down network traffic.
Another option might be to run Master and Slave MySQL servers - I've not done this myself yet (only one customer doing anything with MySQL), but there's plenty of documentation out there including How To Back Up MySQL Databases Without Interrupting MySQL on HowToForge