I've had a look at the Zotero website, and I've had a browse through the Endnote web workbook. I'm not going to sign up for an account as I don't have any reason to use it, and I feel I've got enough new accounts for the time being! It seems like it could be a really useful thing to have - I can understand why students find it extremely useful. When writing my dissertations I used BibTeX in my LaTeX documents, and this has some of the advantages of these tools - it allows you to store all the details of your references, and then formats them for you into the referencing style of your choice. I always found this a great help, and I can see why these tools would be even better - BibTeX requires that all your references are typed manually into a text file, and these tools seem far more sophisticated than that.
It seems a bit odd that users have to enter a comma after corporate authors in Endnote web - this seems a very strange thing to have to remember to do. I'd have thought it would be easier to have a check box to say that the author is a corporation, and then have the software add in the comma for you.
Zotero looks very easy to use from the instructions on the website - citations seem to be added by simply clicking on a button in the address bar. I don't know how this works in practice, but this is how I expected the tools to work. Endnote web looks a bit more complicated, with saving to files and then uploading these files. But maybe you get more functionality with the added complexity. Without a thorough examination it's hard to tell, but I can easily see why either of these tools would be an enormous help to a student writing a dissertation or thesis.