Mac OS X users are familiar with warnings like the one shown here. Apple's "quarantine" has been in place for awhile, and it offers some minimal protection against accidentally opening files which have been downloaded from the Internet.
What most Mac OS X users probably don't know is that Mac OS X keeps a log of all files downloaded. Files are added to that log even if you are using "private" browsing in Safari or "incognito" in Google Chrome, and the log does not appear to ever be cleared.
Even so, Don't Panic: there is no evidence that this information is shared with Apple or anyone else. You do not need to be worried about Apple telling anyone that you torrented all of the episodes of Downton Abbey. The only one who has access to this information is anyone with access to your account.
However, some folks still might find that disconcerting. If you're one of them, you can find the log at ~/Library/Preferences/com.apple.LaunchServices.QuarantineEventsV2 on Lion or ~/Library/Preferences/com.apple.LaunchServices.QuarantineEvents on Snow Leopard (where "~" is the path to your home directory). If you upgraded your Mac from Snow Leopard to Lion, you might have both files.
The information is stored in an SQLite 3.x database, which means that you will need an SQLite editor to read the information (you can open it in TextEdit to get a general idea of what's in there, but it's not very easy on the eyes. --Ed). I have written a shell script showdownloads.sh which will dump the information in an easy-to-read format (note: my script excludes downloads from 'PubSubAgent' which I believe are just RSS feeds). Personally, I find this to be really handy as way to find things that I downloaded but can't remember where I found them.
Thanks to Ben Barnett for bringing this to our attention.