The oldest torrent that is currently still active is a fan-made ASCII render of The Matrix, and it was shared with the internet through BitTorrent on December 20, 2003. For more than 12 years, the same 4.3 gigabyte file has been downloaded by thousands of users, but a recent upswing in shares means that it's not disappearing any time soon.
TorrentFreak reports that the file is 4419 days old, making it the oldest known torrent to be currently actively shared on the distributed peer-to-peer network. The site actually wrote about the same torrent in late 2015, even then saying it was exceptionally old -- with only a single seed keeping it alive, but over 5000 completed downloads.
But, with Torrentfreak's recent publicity, and the sharing-friendly nature of the avid torrenters that have kept the file alive this long, The.Matrix-ASCII is enjoying somewhat of a renaissance in 2016; it now has nearly 200 seeders and nearly 100 leechers. The provenance of the torrent is somewhat cloudy; TorrentFreak say it was shared in December 2003, but an Internet Archive cache of the initial uploader's webpage says it was released on January 16th 2004, with around 7000 downloads between then and the middle of 2008.
The.Matrix-ASCII is the original Matrix movie encoded in text. The finished product is an MPEG-2 file 7989979136 bytes in size, too large to fit on a DVD5. I re-encoded the ASCII movie to fit on a standard DVDR. The two samples are from the larger file and are higher quality. The DVDR is available through BitTorrent. If you wish to download the final movie or either of the samples using BitTorrent with Java installed, I suggest Azureus: otherwise TheSHADOW's BitTorrent Client should work well. You will need a media player that can play MPEG-2 videos to watch either sample and a DVD player to watch the movie.
Using the open-source OpenBitTorrent tracker means the Matrix ASCII torrent should survive the ups and downs of any one BitTorrent site -- and as long as it keeps being shared, it will stay active. At the time of writing, The.Matrix-ASCII has nearly 200 seeds and 80-plus downloaders -- for a file that was first shared to the then-nascent peer-to-peer service 12 years and two months ago, that's impressive. [Torrentfreak]