I would recommend a firewall and anti-virus.
If you are not wanting to spend too much money, AVG Free
] is pretty decent, and... free.
Most web browsers wont automatically download something without your permission, and even if they do, they will only download, not run it.
The real problem I suspect you have is hackers.
An up-to-date anti-virus can assist in preventing this, however not always 100% effective.
The idea of hacking is that you find a bug in a program that no one else has found that can allow arbitrary code to run.
This shouldn't be an issue unless you make yourself a target, by doing things like visiting suspicious sites.
Apple Safari is notorious for having a great many of these bugs, so stay clear of it.
Microsoft Internet Explorer is better than Safari in these respects, but still not very good.
Mozilla Firefox is good. It has had some bugs found, but they are fixed very quickly once found.
Google Chrome is by far the most secure. It uses a "sandbox" architecture that means that even if a bug is found, it is near impossible to execute code from it.
It is not only web browsers that are vulnerable to these attacks. Anything with network activity can be attacked, and unfortunately there is not much you can do about it if you need that program.
But like I said. Unless you make yourself a target by going to dodgy sites or putting your email address that you use for msn/aim/gtalk/... in the public where spammers can get it you should be safe.
1 final thing, make sure that autorun is off for things like CDs and USB sticks.