Kee,
There are several great answers here, but no one has said exactly why you should not store the entire list on your pc.
The reason is that the use of mal-ware has become so prevalent that you can no longer be confident that your pc is secure unless your level of vigilance is essentially on par with professional level network security systems.
The use of software to facilitate identity theft, use other peoples computers to send e-mail/spam automatically, and the hijacking of them to secretly use them as 'zombies' for 'denial of service' attacks has become so common that the AVERAGE open port (access into a computer that has an active internet connection) is 'pinged' (tested) for access every 15-20 minutes (roughly).
Keep in mind that the systems that do this pick the addresses (not e-mail, but your URL) by systematically running through series of numbers by the millions, and check the open ports (an inlet into your pc used to communicate with the internet or printers, etc) automatically day in day out hoping for something accessible. When they find it, they 'push'/upload software that will do their bidding into your computer. The worst form is a keylogger, which will record your every keystroke, and then returns the information to them without you ever knowing it. If you typed key sequences repeatedly in association with 16 digit numbers (as in credit cards), addresses, your name, or an e-mail address, that data will be extracted for testing to see if they can use it.
The only way to avoid these problems are:
1. Us a hardware firewall. Check your router for this, and then make sure it's been set up with passwords. A firewall that hasn't been set up is not a firewall.
2. Encrypt your wireless network if you have one using WPA level encryption (WEP is no longer secure). If you still have WEP, it's worth it to go to the next level of defense and it's cheap. You can get a decent secure router for less than 80 bucks.
3. Use a malware / antivirus filter on your pc, and never hook up to the internet without having it on. Be very, very careful of so called "free" anti-malware software available on the net or through spammed and unsolicited e-mails. Many of them are the exact opposite of what you are looking for and will actively compromise your security.
4. Do not share out files, use, or download software from sites such as limewire and other peer to peer networking systems unless you know exactly what you are doing and what your security is. These are notoriously packed with mal-ware. Even if you are careful, trouble may find you. It's best to avoid this stuff entirely.
5. Make sure that everyone who uses the computer understands the need for security. A 10 year old downloading free games from unchecked sites will compromise your security. So will a teenage boy going to sites you probably wouldn't approve of. People in the malware and computer crime business rely upon the fact that people are tempted by stuff they want when it's available for free.
6. Scan your pc for malware each day and prior to using it for financial reasons. Overkill? Maybe, but not in my own opinion.
These are the reasons your pc isn't safe for storing your passwords - ever. As several people said, the best way to handle it is to write them down on a piece of paper. If you live alone, just leave it under the keyboard. OH - if you are worried about people finding it, then make password that are what they are, but don't write down the entire thing. Pick something that will never change - your year of birth, first crushes initials, whatever, and tack that on the end of each password when you set it. For example: Write down - ilikebbq, mydogisfido, and ilovemygf, but make the passwords ilikebbq55, mydogisfido55, and ilovemygf55. If the list is stolen, or someone finds it, nothing has been compromised.
-Good luck
Kevin