You can use ssh to forward ports onto somewhere else.
If you have two computers, one you browse from, and one which is free to access websites, and is not logged (ie. you own it and it's sitting at home), then you can set up a tunnel between them to forward http traffic over.
For example, I connect to my home computer from work using ssh, with port forwarding, like this:
ssh -L 22222:<target_website>:80 <home_computer>
Then I can point my browser to
http://localhost:22222/
And this request will be forwarded over ssh. Since the work computer is first contacting the home computer, and then contacting the target website, it will be hard to log.
However, this is all getting into 'how to bypass web proxies' and the like, and I suggest you create a new question asking what exactly you want to do.
Ie. "How do I bypass web proxies to avoid my traffic being logged?"