since the server your talking to needs an ip address to be able to service your requests, you cant stop the server from seeing an ip address. However to get around this, there are several organisations that operate to mask the clients true ip address from any server. Most of these charge for the service but there are a few out there. the ones that come to mind immediattely are probably
www.anonymizer.com
www.proxymate.com
these services tend to just use a proxy server to mask the clients address, but if the sites your worried about are blocking any address that makes multiple requests, then that may not help.
Alternatively, theres a site called
http://www.research.att.com/projects/crowds/index.html where your client request is made anonymouse by bouncing it off others who have joined the scheme so the originating ip address is hidden to the server servicing the request.
for more accurate information check out
www.ptclub.com/Anonymousurfing.html
I thinks thats all just about right....
maybe theres others out there who can put me right if im mistaken on anything...
hope it helps
Steelo
btw, it would be interesting to know what it is exactly, that you do!!!