Downloading illegal material is a crime and there are no guareentees that you will not be caught.

downloading legal stuff:

Premium newservers like easynews.com, newscene, etc do not log downloads, thus there is no log of what you download or even what group you downloaded from. they track how much you downloaded and how many times you request a group (but not the group itself). If fact newscene.com has told me their software does not even allow them to log anything more they would have to rewrite to provide those features. Also they provide SSL if you want to encrypt the data tansfereded between you and them. They do keep complete logs on posters, but some only for a limited time

Alot of ISPs do log more things some log what groups you entered, some even the article numbers you request, and burn these to CD.

Downloading from usenet is one of the few areas where there is still some degree of privacy, as long as you pick a good premuim service