That certainly works, but the VPN solution is elegant because it translocates your apparent point of origin to a network in the Bahamas. It can also be configured to funnel 100% of your internet traffic via the encrypted pipe so that somebody would have to be snooping the VPN gateway in the Bahamas in order to intercept your traffic, which would be outside of Federal jurisdiction.
100% of internet traffic includes file sharing/swapping services, chat programs, telnet, IRC, etc; and not just the web. Some VPN clients will even allow you to define exceptions to the rule so that legitimate network use can be broadcast normally over your network, or out to the internet unencrypted.
Quite literally VPN is the coolest privacy tool I've found. Although, I don't see why encrypted connections aren't used for everything already. Even just a simple compression algorithm would be enough to protect most data from casual snoopers.
Not sure about anonymizer.com's record off the top of my head, but some anonymous proxy sites have been known to cooperate with the government when asked for browsing histories (even without a warrant), so caveat emptor.