The Internet has a lot of downsides, in my opinion, due to its mostly-anonymous aspect: flamers, trolls, spammers, bots, and 50 year old guys posing as hot 18 year old girls.
Then again, the anonymity of the Internet has a lot of benefits: bolder discourse through text than in person, broader whistle-blowing, vigilante software development, protection from those that don’t understand freedom of speech and freedom of press.
Given these and many more reasons to desire browsing anonymously, there is Tor. Following the concepts of all the great hacker movies where the “bad guys” start tracing your connection and slowly get closer to you, this bounces your connection from one server to another through its distributed network. This will slow your surfing speed down, but to be anonymous it’ll be the price you pay for the peace of mind your paranoia won’t allow you.