In general no. If a user visits a site you will get some basic information such as browser type, Operating system, referring site, IP address and a few other nick nacks. However - as Pete said if there is spyware on your machine you might. For the most part this is was a problem a long time ago and has been fixed by the various browser developers.

I would suggest you are careful about some of the cookies however. Most cookies are harmless, some are used to track you around the net. If you get a product like Zone Alarm (free for personal usage) or even turn on the cookie prompt for IE, you will be amazed at what websites want to store on your machine.