The design rights for your website are legally owned by the designer who created it. Unless those rights were officially passed to you on completion of the website.
Now most clients do not know the ins and outs of copyright and intellectual property law - why should they? But when it comes to websites you do have to know a few basics just to be sure you actually get what you think you are paying for.
As I said in the introduction the design rights for a website belong to the creator/designer of the site by default. These designs are effectively the intellectual property of the designer who has the right to resell each design as he/she sees fit.
More importantly if you decide to take your website elsewhere you DO NOT have the right to take the design with you. So in some cases what you are paying for is the time taken by the designer to create the design and a license to use the design on your website.
Now I do not want to be accused of scaremongering...so deep breaths everyone...and relax...the majority of website designers do not work like this in so much as they have no terms and conditions in the first place - so nothing is signed or in writing. But if you do have terms and conditions with a website design company it might just be worth finding out who actually owns the design rights.
Oh and be sure to check out clause 9.2 of our terms and conditions.