What happens if caught?
Depends on where you live and your ISP. Cox Communications will send you an e-mail telling you not to do it again then delete all records of the event (after my first warning e-mail I called them to ask what they were going to do and they had no clue what I was talking about so I'm assuming they deleted all trace of the event... and I've received 3 of these e-mails btw, 1 of which was for something I didn't even download). Now if your ISP does give out your info, then you'll have fines, probably a lawsuit, and possibly jail time or, if the judge goes easy on you, community service. The jail time and community service is mostly for people distributing the files though, not the ones downloading the files.
How often do people get caught?
Using torrents and other peer2peer programs, people get caught by the hundreds (probably thousands) every day. As for using filesharing sites like megaupload and mediafire, I have never heard of anyone getting caught for *DOWNLOADING*, but I have heard of people getting in trouble when *UPLOADING*, but even then I've only heard of that happening on rapidshare on very very rare occasions.
How easy is it to get caught?
If you are using anything peer2peer it's dead easy for them to catch you because peer2peer, by it's very nature, requires for everyone to have everyone else's IP. However, copyright violation is a civil offense, not a criminal offense. Your ISP is not required in the USA to give out your personal information unless you committed a criminal offense. So anti-piracy groups can get your IP, but they can't turn that into any kind of real information like a name or street address unless they can get you on criminal charges as well or if your ISP is a pushover. Using filesharing sites like mediafire and megaupload the only way they can get your IP is if the site gives it to them, and they are not likely to do that for piracy... though they might for something like the blueprints to the pentagon or something along those lines =P.
Do they track every download you do?
No. What they are currently doing to catch pirates is going on p2p networks like torrents and gnutella and logging all the IPs that are downloading or uploading certain files, then sending letters to those people's ISPs. So they track it by the file, not by the downloader.
Now there has recently been some talk about how an IP address might not even be enough evidence to convict someone because of the growing number of unsecured wireless networks. So if you have an unsecure wireless network and get in trouble, just deny everything and say it must have been a neighbor.... they can't prove it wasn't a neighbor and they can't get a warrant to go search your neighbors' houses. Under the concept of "innocent until proven guilty" this is a perfect defense, however if you are on civil trial I believe (but I'm not 100% sure) you are actually "guilty until proven innocent". Since copyright violation is a civil offense you might get off the criminal charges which include the fine and everything, but you'd probably still lose the lawsuit.
It's really difficult to say for sure because anytime someone is sued or otherwise gets in trouble for piracy, either they are a member of "the scene" and get in BIG trouble because of all the criminal stuff they've done (scene members also tend to get into other illegal things like fraud and such), or they are a clueless nobody who doesn't know which end of the mouse plugs into the computer so they confess up front because they don't know how little proof is really against them.
I however can personally testify that Cox Communications doesn't give a rat's right foot if you pirate or not.