When using LimeWire you were not downloading files from sites. The Gnutella network is a protocol where people are able to connect to each other using any of the gnutella programs such as LimeWire, Phex, etc. and share files. Person to person, peer to peer, p2p.
The official LW site is not allowed to distribute the actual program. However the program can be obtained via other sources. Look around and you will find such links on these forums.
I'm still happily using LimeWire. I am presently using the LW Pirate Edition;
http://www.gnutellaforums.com/gettin...e-edition.html. You can also still use any of the LW 5.5.10 or earlier versions if you use one of the connection fixes that can be found on these forums. (Any version between 5.5.11-5.5.16 had auto-update functions which force it to stop working.)