The different numbers of connections you see depend on whether you're connecting as a leaf or as an ultrapeer.
When you're a leaf, you connect to either 3 ultrapeers (LW basic) or 5 ultrapeers (LW Pro). Ultrapeers are people with relatively fast connections who handle more of the search traffic & shield the leaves from unnecessary traffic (so the leaf sees searches which relate to files that they're sharing).
Peers are other ultrapeers!
When you're connected as an ultrapeer, you'll start off connecting to around 23 peers...ie other ultrapeers. Then, more leaves & peers will connect over time...there can be around around 50 connections in all.
The network decides who connects as an ultrapeer. Providing you're not firewalled & have a reasonably fast connection, if the network needs ultrapeers then you'll connect as one.
I'm not sure that there are any big advantages to being an ultrapeer, you tend to see fewer uploads but searching might be a bit better when looking for rarer files. Have a look at stief's post below.
http://www.gnutellaforums.com/216153-post5.html
And if you want a better explanation of leaves & ultrapeers, have a read here.
GnuFU en - Gnufu
This info is from the BearShare technical FAQ, & is a good explanation of both connection types
