debian jessie – How to backup a remote server running?

We want to make a backup of everything on our server, which runs remotely from the other side of the world, without closing it.
(This is a Debian system.)

A lot of the backup tips that I see, like using not a word, seems to presuppose that the reader is disassembled and unused. But am I not supposed to exclude "live" directories such as / proc and some subdirectories under / var (however, some elements under / var, I know that make need to keep) and / mount? What else should I think of in this situation? Then I guess I can just take it with rsync and using a bunch of --exclude flags.

Or are there better ideas, especially those favoring free software?