If users view documents on my website (for example a pdf file that represents some confidential information), is there anyway I can prevent them from saving the document locally?
In a word - no.
Once you've sent the data to their browser they can do what they want with it.
You could use some Flash Component or Java Applet to make it harder to save the information but they could still take a screenshot of the browser and save that locally.
The only practical approach is to ensure only trusted users can access the information (which you're probably doing already).
This is very difficult. Off hand the most effective thing I can think of would be to deploy a Java applet that displays info by way of downloading it at run-time
But that still won't prevent users from taking screenshots and saving those.
If you are that concerned about it, you should not make the confidential data available or at the very least available in a downloadable format.
Once the user has downloaded your PDF (to the browser) they can do anything with it. They can save it to elsewhere in their hard drive. Even if you somehow disabled this anyone could intercept the network traffic using a third-party application and save the PDF that way.
Your best bet is some kind of Digital Rights Management tool to stop the user from distributing the PDF even if he or she downloads it. For example, FileOpen or Adobe Content Server. As you can see, such tools can (technically) prevent printing, force the content to expire, etc.
Note that this is most useful for users who are likely to accidentally download or distribute the data. Malicious users may be able to circumvent these restrictions, e.g. bypassing the print restriction by taking a screenshot of each page and printing that instead.
A relatively easy way to prevent this from happening by accident is to hide the toolbars and menus when the document opens. See this question/answer on the Adobe forum. Of course the user can get around this if they know how and a determined user can circumvent just about any restriction you place on the document if they have rights to view it.
If it's in a work network, I would suggest you implement Active Directory, if you haven't already. With Active Directory working, you could easily configure user's default profile path, having that path on a file server. That way, all the applications by default will save into that path instead of the local hard drive. Hope it helps.
Not a solution, but an anecdote. Several years ago a friend of mine had compiled a lot of sensitive internal information into a Word document, and had watermarked the pages with "FOR INTERNAL USE ONLY" and locked it.
A couple of days later she got a phone call from the sales manager.
"How do you unlock this Word document?"
"Why?"
"I want to take the watermark off so I can give it to a customer..."
Head -> Desk - Thump!
It's a tough issue.