When I have two mysql servers that have different jobs (holding different databases) but want to be able to use one of them to slip in when the other one fails, what would you suggest how I keep the data on both of them equal "close to realtime"?
Obviously it's not possible to make a full database dump every x minutes.
I've read about the Binary Log, is that the way that I need to go? Will that not slow down the fallback server a lot? Is there a way to not include some tables in the binary log - where it doesn't matter that the data has changed?
Binary log is definitely the way to go. However, you should be aware that with MySQL you can't just flip back and forth between servers like that.
One server will be the master and the other will be the slave. You write/read to the master, but can only read from the slave server. If you ever write to the slave, they'll be out of sync and there's no easy way to get them to sync up again (basically, you have to swap them so the master is the new slave, but this is a tedious manual process).
If you need true hot-swappable backup databases you might have to go to a system other than MySQL. If all you want is a read-only live backup that you can use instantly in the worst-case scenario (master is permanently destroyed), Binary Log will suit you just fine.