Technically it's possible to hide yourself completely while downloading a torrent by leeching (disabling upload), but that is generally frowned upon by everyone and will slow you down anyway. One could go through the trouble of finding less popular trackers, but ultimately the best advice is to not download illegally. As for OP ... don't bother pooping your pants. The worst that can happen, as others have pointed out, is that if they catch you again in the future your ISP decides to terminate your account and you'd have to find a new ISP. They're not going to sue you, unless you have music and it's the RIAA that's coming after you. Those guys are a bunch of litigious pricks, the scum of the earth.
The ISP has a legal obligation under the DMCA to stop copyright infringement. If they don't, the RIAA or any other group can sue the ISP. They're not doing this to arrest you, but to cover their own asses.
I got the same sort of email about a year ago from my ISP. It was from NBC about two episodes of "The Office" I was downloading. I filled out their little form saying I deleted the files, and I just gave up downloading while I have this ISP / IP Address (I have a static IP). I think the email had said something regarding a lawsuit if they catch me again. I pretty much only downloaded "The Office" and "Hell's Kitchen" anyways, so I just figured it wasn't worth the headache. I download a fair amount of stuff from iTunes now, and I'm okay with paying $1.99 per episode to ensure I don't get a lawsuit. I actually really like the convenience of it too, ttytt.
download peer guardian. Sucks though, these big corporations use fear as theirpeimary weapon nowadays. Find someone, use them as a scapegoat by suing them a large sum of money, make the case public, and send out these emails that scare people. I would imagine that if you still download stuff your chances of getting caught are less than 1%
i use peer guardian also. i dont know how helpful it is as i've never been caught with or w/o PG, but i run it whenever i dl torrents and whenever im done i always see a bunch of blocked IPs from anti-p2p networks.