Optimize Your Computer

These are some tools and a regular clean-up process I recommend for all computers that access the internet. (Note: This is intended for computers running Windows.)
Just how often should you schedule this process? It really depends on where the computer goes on the internet. Generally speaking, the more flashy advertisements a site has, the more junk it will leave on your computer. This is usually limited to advertisement content, which can take up space on your computer, but won't intrude on your work or cause noticable slowdowns.
What you really need to watch out for is the stuff that is downloaded and installed that causes the problems. All those free screensavers, icons, and other "cool things" are notorious for including "spyware", and other malicious components.
In general, I recommend doing this process as soon as possible, and then doing it again about a month later. Pay attention to how many problems came back after a month. If you have a pretty good amount (25+) serious issues, plan on doing it again in a month. But chances are that there won't be too many problems, so wait about 3 to 6 months before doing it again. Even if you're not seeing any new problems, it is a pretty good idea to plan on a doing this process at least once a year, just to make sure nothing sneaks in.
(If you see a lot of serious issues, you may want to consider more serious action, like contacting an IT professional to check your computer out.)

Now that I've warned you about downloading and installing free stuff from the internet, naturally the best way to deal with the problems is to ... well ... download and install other free stuff from the internet.
Okay, seriously, I personally use these tools, so I'm comfortable recommending them to you.

Here are the tools I recommend running on your computer, in the order you should run them:

1. Adware Removal
   AdAware by Lavasoft
   Advertisements can leave files on your computer, usually for purposes of trying to customize ads to your interests. In addition to cleaning up these files, AdAware does some spyware checking and cleaning as well.
2. Spyware Removal
   SpyBot S&D by Safer Networking
   Focusing on the more malicious problems, spyware is software that gets on your computer and runs without you knowing it
3. Registry Cleaning
   Free Registry Cleaner by Eusing
   The Spyware and Adware tools will examine your registry for problems related to advertisements, but the registry cleaner can get rid of wasteful registry data. There's a good case to be made that this should run before the other tools so they don't waste time scanning something that's going to be removed anyway. However, I've seen spyware maintain things in the registry that a registry cleaner will delete, only to have it put right back in by the spyware. So it's best to clear the spyware out first.

Defragmenting
On the subject of optimizing, it wasn't very long ago that you would hear often how you should "defrag" your computer regularly to improve performance. Defrag is short for "de-fragment", meaning to organize things together in one place rather than splitting them up. Basically, if things are split up, it takes the computer a little extra time when it needs to go around and gather things together.
Just a few years ago, the majority of computers were starved for hard drive space. It was pretty common that when you needed to install a new program, you would need to remove other things to make space. This is the usual source of fragmentation, removing something creates a 'hole' in the used hard drive space, so when you installed something new, it might get split up between the 'holes'.
Currently, most computers have a pretty good amount of space available to install new software. So the fragmentation never becomes a serious issue.

So defragging is still good, but it may not be very effective.