I am looking to clone several servers periodically as part of a backup scheme. Is it possible to clone a server that is in use using clonezilla or other foss product? One of these servers is running an sql database, I'm not sure if this would add an additional variable to this situation.
Tricky as there will be issues with open databases and other files. The VMware Converter can in theory clone running machines but in my experience this is a bit hit and miss. Beyond that you are looking at specific apps and procedures as Journeyman Geek hints - and these can be a bit pricey. If the servers can be shut down for a short period you could run Clonezilla on the disks to make copies and then use 'regular' backup tools to keep backups of what's changed since the drives were cloned.
Our backup strategy for some servers is to make virtual copies of them (using the VMware tools) that can be fired up at a moments notice and then have a regular backup of the changed data restored to them very quickly.
Ultimately your implementation choice will depend on the amount of service continuity you need - and the depth of your pockets - give us some more info on your scenario.
With windows, there's one thing you absolutely need to have in a backup solution where you don't want to shutdown a system- volume shadow copy. Windows backup on windows 7 (which 2008 r2 is based on) supports it natively - so i'd probably go for the native backup solution on that.
For the windows 2003 system, any decent disk imaging software such as acronis should probably do the trick. I've not actually had much luck or experience with the built in backup system on xp or 2003, but i believe they do volume shadow copy as well.
The reason people generally take down a server for backup is database consistancy- you want your pre-backup database and your restored database to be the same - if you have a few hours where there's no data added to the DB, you should be fine, as long as the backup takes place before that period ends.
If you have the time, you absolutely should try running a test run of the backup/restore procedures, and keep a duplicate offsite copy of any backups if possible - that way, even if your main backup goes pear shaped, or gets destroyed you have a backup.