How do I prevent someone from monitoring my Internet activities from another computer?

Good question! Since nobody knows exactly all the resources hackers know to monitor or steal information from other computers, then the best thing to do is prevention.

To prevent unwanted access to your PC:

1. Keep up with all the security patches and updates for Internet Explorer and your Windows version. You can find this updates on www.microsoft.com in the support and downloads sections. If you use WinXP you can "automatically update" configurating the right settings.

2. Buy and install an "Spyware" tracking software. You'll find dozens of them, but I recommend what I use: SpyWare Nuker. Great software!! It also gets rid of adware and spy-cookies.

3. Watch your "sharing settings" on peer-to-peer software like Kazaa or Emule. This can be an open door in some cases, so watch what you share. It's amazing but some people share their whole harddrive on this programs.

4. Optional. If your information and activities are serious business, get a firewall. A firewall is a software (that is sometimes integrated to routers and modems) that blocks access to your PC via encryption. Firewalls are affordable nowadays, you can get one for less than $100 (of course they can go up to thousands depending on how sofisticated you want it).

Hope this helps! Good luck.

I use a host of free stuff but I don't have problems.

Zone alarms firewall
http://www.zonelabs.com/

reactive spyware removal:
SpyBot Search and Destroy http://www.spybot.info/en/home/index.html (Caution: Not for WinME!)

Proactive spyware prevention:
SpywareBlaster
http://www.javacoolsoftware.com/spywareblaster.html

AntiVirus;
Norton system works 2003.

These can track and remove many keystroke loggers and other nasty stuff.

A hardware firewall (a.k.a. Router) can also help isolate your machine from intruders.

Keep in mind, if you're referring to a computer at work, take every precaution to keep your work safe and your harddrive clean, of course, but there is NO RIGHT TO PRIVACY on a machine owned by your employer.

To add on to what Astaroth said, also keep your File and Print Sharing settings in check. It's really easy to access your home network from outside the network in this case, if you don't have a firewall. The majority of routers now have firewalls these days. Good free software firewall: Zone Alarm. Also, make sure you have good anti-virus protection (AVG from grisoft, it's free and good. Clamav for unix users). Above all, if you have any sensitive information, keep it backed up off of your computer (CD, external hard drive, etc).