Limewire has fewer users than Morpheus. Kazaa and Morpheus (basically the same thing) are probably the biggest since Napster's glory days. The current PC Magazine reviews several of them. They rank Morpheus #1 and WinMX #2. BearShare and Limewire both use the Gnutella network according to the article.
Kazaa also installs spyware on your computer without allowing you to opt out. Morpheus doesn't do this and uses the same network that Kazaa does so I highly recommend morpheus over kazaa...
Kazaa allows you to do 15 free searches from its website (or at least they used to) and you can download from there ... w/out having to download the kazaa software and registering. Kazaa and Morpheus use the same database to search for the files. Morpheus is better (im not exactly sure in detail) because it will search and find all bit rates or something compared to Kazaa which limits to 128 or something like that.
Limewire is a client for the Gnutella network. Other clients include gnucleus and Gnotella. I use Gnucleus in windows. Limewire installs spyware, and is not open source, whereas Gnutella is. Only problem is that Gnutella crashes on occasion. But I haven't had it crash once since 2 releases ago.