The short answer is everything and you can't do anything to stop it.
Another short answer, in your case, is to do the following and after that not think about it too much:
1. Install a firewall, antivirus, and antispyware, and keep them current with automatic updates. Either buy one, for instance, Norton 360, or download free ones.
A simple setting of Comodo as firewall and AVG or Avast as antivirus (all free) is a good configuration. You would also need anti-spyware, though this is starting to be included in firewalls or antiviruses, for instance in Comodo.
2. Clear cookies and cache. The simplest way to do that is to use firefox, which is in any case a much safer browser to use. Download it from: http://www.mozilla.com/en-US/
After browsing and wanting to clear your tracks, go to tools in the upper menu and choose "clear private data" and check the boxes of cookies, cache, and browsing history and then press ok.
3. Protect your passwords. I assume you let the browser keep your passwords. Adding a general password to protect them helps a bit. In Firefox, go to tools/options, press the security tab, and then press create master password. I would make sure to remember it though as otherwise you loose all your passwords at once.
Ok, you are now pretty safe. Are you really - not in the least, but it is pretty much as good as you'll get so I wouldn't worry about it too much. Check your credit card statements, as you needed to anyway also without browsing the net. Now you can safely browse and shop online, or as safely as you would offline (check to see you are buying from a reputable shop and so on).
The long answer is longer.
Who is it you are worried about spying on you? I don't see much in your profile and will answer more generally:
1. Family & Friends - Very hard to stop if they really know what they're doing. Otherwise previous recommendations would probably work.
2. Your goverment. Forget about it, you can't really. There are techniques to improve security like the tor network, but it doesn't work so well and you need to know what you are doing.
3. Online criminals. Here the advice I gave above mostly works. If they target you specifically there is nothing much you can do. If not, in order to get your credit card information and your social security they don't need to follow you online, it is much easier and more productive to crack places you shop at, universities and so on.
4. Google. Don't use Gmail and some other free services they offer. You can now opt-out of them leaving a cookie on your machine in certain cicrumstances. If you don't use gmail, you can go, in firefox, to tools/options, the privacy tab, in the cookies part press exceptions and there you can add to block their site by adding it to the exception. They still will know a lot about you, but a tiny bit less.
To summerize, there is never fullproof security, but what you want is to deter the simplest kinds of spying.
Moreover, the advice above: firewalls and antiviruses, are also good against viruses that can delete all your information on your computer, or make your computer into a robot working for the mob like so many innocent computers (which also makes it run much slower for you).
Hope this helps.
