A company that I previously worked for (full/part-time) is wanting to list me as a contractor on their website. I built the website originally and they wanted to have an area with a name and picture of all of their contract employees. I find this a bit uncomfortable and strange... is that just me? I feel as though if you're a contractor or freelance then the whole point is to avoid being tied to a business. Am I wrong in feeling this/not wanting myself to be listed?
Isn't that why they're asking you? Or is it more of a demand? You have every right not to be listed there. The choice is completely up to you whether or not you want to be associated with them or not (unless you signed a contract saying they could list you, in which case you should have read the contract).
Honestly, if I ever hired anyone to do something for me concerning my website, I would ask them if they wanted to be mention in the credits in some way. It's just polite. There's nothing wrong with them wanting to recognize you. If you don't want to be listed, politely tell them that. If the person refused, I'd probably just fill it in with something anonymous like "He Who Shall Not Be Named" just to tell people someone helped with this but didn't want to be mentioned.
For a lot of large corporates it is absolutely normal - it can work in your favour as well as theirs. Assuming the contractor and company have good reputations it is a win-win situation.
They can associate themselves with known good contractors - helping their shareholders gain confidence in the company.
As a quid pro quo you get a free reference (after all, why would the company want your name up there unless they were happy with your work) so you may be able to use this in future.
To answer the question: No it is not 'normal'.
It indicates that they want to maximise their marketing, advertising and public image through such efforts.
Most companies (in my experience) focus on their products and on contributions by current employees.
So it's not normal. As to my 'opinions' about it (what most other people are giving), I think it is fine if you are proud of the work and happily putting on your own resume and talking about it.
If you actually have no need for it yourself and no need for the visual reference for future work I would tend to be a little wary and maybe question that a bit more to see exactly where they are coming from. If you don't want your personal information their (and a photo counts as that), let them know and they'll probably comply. If it was a real issue you could potentially take legal action but for your situation that's unlikely to be wanted, warranted or needed.