If we are talking in terms of acquiring things that you should probably be paying for;
Direct downloads we are all pretty familiar with the risks. IP session logged with details of your activities on the host site. Possible corrupted file(s), viruses, etc. Something you should take into consideration that a lot of people don't think about are honeypots. Most of the time honeypots are set up to catch a hacker in the act of attacking a website or network, but they are also baited with downloadable content as well. Such as a music directory. Most of the time, the police will not act on small stuff. Problem is there are just too many people downloading a very few number of files (ex: like 3 songs a month). But if you are someone who SERIOUSLY gets into this game, direct downloads are not going to be good for you. On the reverse, black hats use similar techniques to increase their botnets (ex with clickjacking). Old school trojan infection for the lulz and flipping your screen upside down or flashing pron is dying. They don't want you to ever know they have you!
Torrents are generally much faster and 'can' be safer vs. the corrupted files. That is unless whoever has the file chooses not to get rid of it and continue seeding. It is also a bit more difficult for police to track torrent activity. But only a bit. Remember with torrents you have to download the torrent THEN the file you want. The torrent itself could fall into the above description. As for the file itself, the more seeds the better, usually. IP sessions are still logged, but with an active torrent client open there is going to be a lot more traffic to sift through, which will spiderweb to various other people. If you pull a file from 1 or a only a couple of seeders, that means more direct connect time, more information of your activities logged and longer chance of being actively traced. Black hat viruses with torrents can screw you very hard. For example, you pick up 1 corrupted song with script that disables your options, increases your upload to max, downloads as many pre-placed viruses as possible with attractive/same-like names (like games, music, movies) and seeds the shit out of them. You computer is now a breeding ground for infecting seeds and that traffic CAN be traced directly back to YOUR computer.
So which is safer? Meh, its about a 50/50 in my opinion. Torrents are harder to track down and require some clever coding from black hats. Direct downloads are easier but are easily detected. If someone isn't downloading a whole lot they have a better chance of staying under the radar and clean from attacks. But there is always a risk involved.
"The quieter you become, the more you are able to hear..."
"Drink all the booze, hack all the things."