#Bibbase
Bibbase
I think that BibBase would be a perfect solution if you can at least run CGI scripts; instructions can be found on this page (if you can run PHP then it's even simpler). You need to feed it a Bibtex file, but if you use Mendeley then it can automatically grab it from there.
Update: Bibbase now allows you to use just javascript. (h/t ChristianF)
BibBase makes it easy for scientists to maintain their publications pages. As a scientist, you simply maintain a BibTeX-file of your publications, including links to the papers, and BibBase does the rest. When a web user visits your publications page, BibBase dynamically generates an always up-to-date HTML page from the BibTeX file, and even allows the user to sort the publications by other than the default ordering (e.g. year, author, keywords, research area, publication type).
Here is an example of the output.
A custom alternative
I happen to have a departmental server that doesn't allow PHP or CGI; you can read about what I do to solve this problem on my blog and see the kind of output generated on my group's site. An even more jazzed-up version, which is searchable and filterable, is on my own site.