You mean like not pissing off an employer by violating company policies and being fired without a reference?
I fully agree that you shouldn't do anything outside of company policy, hence my reason for giving my disclaimer, and then the answer to how they could do it. So if it's against company policy or somehow illegal, I don't recommend they do it. If it's neither of these, then they have a working solution for getting around the problem.
And, depending upon where the individual works, violating a state or federal law or three?
I'm guessing you're referring to the "anti-circumvention" laws? Hmm, I can see your point, but if I remember the laws correctly, it only applies if you "break" the protection, not go around it. SSH tunneling doesn't actually break the security, and thus it's not considered illegal. At least I haven't seen anyone at the Fed say so yet. But then again, I haven't been a sysop in a few years, so that could have changed. I'm just commenting on my last and best available knowledge.
Now, back to the OP. I didn't happen to think about this before, but
SaraKC, can you tell us what this site or sites are that you can't get to anymore? Also, is there a company policy that tells why said sites are blocked from work? If the sites are rather harmless (like this one for example), they may be blocked simply on the grounds of a list recommended by a security company because said site(s) fell under a specific criteria which the admin and/or bosses wanted blocked, and thus it got blanket banned with a variety of offending sites.
Case in point. Back at the company I worked for, sysops, tech support, and operations all had access to AOL Instant Messanger (AIM), ICQ, and most other instant messaging clients. Partially because we used them for communication between desks and departments (and states), and partially because we needed them for customer interaction from time to time. We also had almost complete, unhindered web access in order to do our jobs. Customer Service however had ZERO access to IM, only 1% access to the web (ie, they only had access to a few public sites they needed to do their job, plus any corporately hosted sites) and our central database because if they didn't, the CS reps would goof off or ignore customers while they IM chatted or surfed the web. They also tended to naively go to sites that introduced viruses into their machines, and ultimately the network as a whole.
So I would probably first start by getting internet access at your home. If that's not possible, discuss your reasons for using company computers and internet for personal surfing with your boss and/or sysadmin. If they allow you to do that, use the SSH tunneling I showed you. (friend with net connection and server required) But if they don't allow you to do anything like that, consider using either the library or an internet cafe. You could also use the free internet connection at a local restaurant or store. Just be sure to do it by their rules, which usually involves a purchase prior to use.
There's lots of different ways you could go about surfing the web for personal reasons. Just be sure you use the legal methods.
PS to Mods: Sorry if my first post sounded like I was condoning the OP to do something illegal. That wasn't my aim. It was my assumption that they would or had done what was right and checked all the proper and legal avenues first before proceeding. I will endeavor not to make such assumptions in the future.