Basically there are two main types available: async snapsnots and fsync()
. They're called RDB and AOF respectively. More on persistence modes on the official page.
The signal handling of the daemonized process syncs to disk when it receives a SIGTERM for instance, so the data will still be there after a reboot. I think the daemon or the OS has to crash before you'll see an integrity corruption, even with the default settings (RDB snapshots).
The AOF setting uses an Append Only File that logs the commands the server receives, and recreates the DB from scratch on cold start, from the saved file. The default disk-sync policy is to flush once every second (IIRC) but can be set to lock and write on every command.
Using both the snapshots and the incremental log seems to offer both a long term don't-mind-if-I-miss-a-few-seconds-of-data approach with a more secure, but costly incremental log. Redis supports clustering out of the box, so replication can be done too it seems.
I'm using the default RDB setting myself and saving the snapshots to remote FTP. I haven't seen a failure that's caused a data loss yet. Acute hardware failure or power outages would most likely, but I'm hosted on a VPS. Slim chance of that happening :)