What are the considerations for backing up my Domino server?

This depends on how much you're willing to spend. If you have an enterprise backup solution that backs up all of your servers onto a shared system, you're probably in good shape. Most of those packages come with a Domino backup agent that lets you back up the database while its open.

If you're using the operating system's generic backup utility, you're going to have to take down the server processes in order for the backup to adequately back up open files. There are several databases that are constantly open, and they are critical to the operation of your server.

Remember that replication is not a replacement for a backup. What you can do, however, is replicate all of your databases to a server that gets taken down at a specific time to be backed up. You still want to do a periodic file-system level of all servers, though.