Real Media is one of the granddaddies of web video. They've been around for a while, and bought Vivo who were their original competition. Real has a bad reputation because their player sends data back to the Real server about what you watch, but only the truely paranoid will have an issue with this; the data is trivial, and pretty much everything reports back to someone these days...
The good thing is that Real provides by far the best image quality over the other formats, but there are some drawbacks. Real is largely cross platform (which means you can get the player for most Operating Systems) but plays in it's own window. There are two main versions of RealVideo; Real8 and Real9. They tell me that Real 9 has better image quality and smaller files, but I've not noticed so far. This leads to the second Big Lie:
Big Lie Two: Always use the most recent codec.
The best practice is to encode into the last but one codec. There will always be a larger installed user base for the older version, newer versions are backwards compatible and people might not want to wait for a new player to download. I always use Real 8 two pass encoding, but here's a selection of clips to show the differences:
Real 8, One pass, 100kbps, 133KB
Real 8, Two pass, 100kbps, 129KB
Real 9, One pass, 100kbps, 130KB
Real 9, Two pass, 100kbps, 129KB