If
1) you're using your own account you've got with your ISP;
2a) you've given your ISP your real name and address;
and/or
2b) you dial in from your home phone;
3) haven't spoofed your IP address;
4) the law enforcement agency has a legal reason for
wanting the information from your ISP;

it's a simple matter. It doesn't matter if you've got a static IP address or a dynamically assigned one. Your ISP keeps a detailed log of who's connected when, and what IP address they had at the time. It's just a small, quick search in the database.

I have done this as a job. One of the more notable cases I had was where a kook was threatening our Department's minister. We got him! Turned out to be some harmless young fool.

Mind you, the average Joe Bloggs on the street can't (legally) obtain this information. If someone works in law enforcement and they have a legal reason to obtain the information, the ISP MUST comply.

If you're going through an HTTP proxy in some distant, hardly even heard of country (like outer Mongolia or Woop Woop) who is unlikely to comply with handing over their records (assuming they keep any), it becomes harder, but still not impossible. Nothing's impossible in the land of internetworking.

Another difficult situation is where the person you're trying to track down uses different Internet cafés, public libraries etc. to do their dirty work from.