Over the past year or so, a program called BitTorrent has exploded in popularity amongst the anime fansubbing community. You download the BT program, find a site with files you want, and you're off!

In terms of anime, BitTorrent is generally best for grabbing new releases from your friendly neighborhood fansub group. Want the newest episode of Bleach or Mahou Sensei Negima? Your best bet on finding them, other than good old IRC, is probably BitTorrent. If you're hunting for an episode of Saiyuki or anything else that's been licensed, though, you probably won't find it. And files that are more than a week old become harder and harder to get, usually.

BT's a bit interesting in the way it works. It allocates all the space needed for the file, before you even get it. It then downloads the file in random pieces as it can get them from various seeds and fellow downloaders. It's a shared resource -- you're simultaneously downloading the file and uploading the file to others.

You can get BT here: http://bitconjurer.org/BitTorrent

places to get anime:

(http://a.scarywater.net/akeep) Anime-Keep's a pretty decent source, with lots of stuff for you to DL.
(http://www.animesuki.com) Anime Suki is a good centralized place to find different group's torrents.
( Tokyo Toshokan is another listing of various torrents.
(http://bt.saiyaman.info/) SaiyaMan has a large selection of raw/untranslated anime for your perusal, uploaded shortly after their original air date on Japanese television.
(http://www2.l33t-raws.org/phpBB2/torrent_list.php) l33t-raws is another source for raw episodes.

If you find any other good sources, /msg me and I'll add 'em to the list. Hope this helps!

(as always, it's infinitely better to buy the anime. If you don't have any other way to get it, or you're desperate for the latest releases, BT is a good way to go. The ethics of fansubbing can be rather shady and questionable at times, but the cardinal rule is that, if you can, try to support the original creator with a purchase. If you like what you watch, either buy the original or wait until it gets an official translation in your country of origin.)