I am having the same problems as others posting here, but I wanted to add my experiences because I think it will help from going down the wrong path.
First off, I just want to say that Bit Torrents are legal, just don't download copyrighted material when using it. I download Open Source software (Like big Linux Distro ISO's) all the time.....or at least until I started having these problems.
Anyway, what I have found is this......
It doesn't matter if I use Azureus or uTorrent, (on my desktop) they both do the same thing. If I leave a torrent running overnight, it not only kills my Internet connection (all computers in my house can't access the Internet), but it also kills the network connection on my LAN (my workstation can't access my local server). I know this was mentioned before, but please bare with me. If I simply kill my Torrent app, my Internet connnection does not come back, but my LAN connection does. I must reboot my DSL modem for my Internet connection to come back.
On the other hand, if I only leave my Torrent app open for a little while (a couple of hours or so) it will run fine for a little bit and then I will loose LAN connectivity, but not Internet for the whole house. At that point, all I have to do is close the Torrent app for my LAN connection to come back.
Okay, here's the real kicker. I can run a Torrent client (either Azureus or uTorrent) from my Laptop (running the same OS levels as my desktop) just fine without any problems at all. I leave it running for days in a row without problem. I can also reboot my desktop into Linux (running OpenSUSE), running Azureus and I can download Torrents with no problems at all.
All this being said, I can't see how it is anything but a local workstation issue. Possibly a setting in Windows, my Torrent apps or maybe another app that I have installed on my desktop. I haven't done a packet trace on my workstation when it is having a probelem, but it must be sending out a packet (or many packets) that end up killing my modem.
Sorry for the long explaination and I know I repeated a lot things already mentioned here, but hopefully this ties things together a little more. I don't think it is a problem with the modem, router or anything like that. I will do the packet trace and follow up with my results.