Yes, it is possible. I am not sure if they can provide a copy. They certainly won't unless you go to the law.

Absolutely, I'd be surprised if they didn't keep a record since it's data that the police or other gov't agency could request. Getting a copy might not be so easy though... my guess is that your web history is jumbled up with everybody else's, and you'd probably have to pay them to extract a report of just the places you visited.

It is possible for your ISP to trace or see websites you have visited. If they received a court order to do so they could certainly perform this trace and log all of your Internet activity. Any Internet service for which you receive a bill (or have your personal information linked to in any way) is not completely anonymous Internet service. Where you might feel relieved is that it is highly unlikely that the average ISP logs your online usage, other than as a simple measure of bandwidth. Logs take up space and processor cycles, depriving ISPs of resources needed to keep their service equal to or better than the Internet service provided by other providers. However, an even more important point is the concept of "net neutrality", where ISPs agree to adopt a "common carrier" approach and allow all Internet traffic of any kind through their wires. Logging is the first step towards filtering, and filtering means the ISP is regulating your content, which means they become liable for your content. If the ISP doesn't concern itself with your web content (without a court order, that is), then they won't be sitting next to you at the trial as a co-defendant. EDIT: You can install network monitoring software on a particular personal computer which logs Internet access and thus will tell you what web sites that particular computer was used to visit. Such software exists as a less aggressive option for parents concerned about their child's web surfing, as opposed to more aggressive approaches such as actual blocking of sites which may have adult content. Direct blocking may hamper your child's proper education depending on the aggressiveness of the blocking software, such as blocking 19th century literature websites which contain book passages such as "the great boat BREASTed the waves". Network monitoring software can also be used by individuals who don't visit adult websites but who may be concerned that malware on their computers is doing so for them. Note that network monitoring software does use processor cycles and RAM like any other application, so like the ISPs you should probably only use such software if you have a current concern about potential misuse of your Internet service.

why, been downloading things we shouldn't have?

All you have to do is look at your history or local host files, this will tell exactly where you have been. No need to go through you ISP.