I've gotten a total of three letters since 2002, on three different computers, for three completely different files. The first time, in 2002, I was using my roommate's PC to download Metroid Fusion for GBA, using iMesh (anyone remember that?). He got a pop-up letter from his ISP saying to delete that particular file. He did, and nothing further happened.
The second time, at a different place, in 2003 I got a letter from Nintendo saying that I had downloaded Zelda - Four Swords for GBA, using a random ROM site. Same thing, deleted and no further contact.
Third time was this year, using torrents, downloading Metroid Prime 3 Corruption for Wii. Again, different place, different provider. This time, my entire internet connection was suspended and when I tried to open Firefox, my homepage was replaced by a letter from Cox Cable, specifying what file I had downloaded, and even where it was on my hard drive, demanding that I delete it. My roommate couldn't connect to the internet, either. I was using a wireless network adapter, and he was hardwired to the cable modem. Unsurprisingly, I deleted the file and our service was instantly restored.
What concerns me about my own experience is that only Nintendo games have triggered any kind of service interruption so far. Perhaps they're just more savvy about people stealing their games.