It depends on what you mean by upgrade. There are a few things you can do to upgrade without opening it up.
1. Get a faster internet connection. In most areas cable is fastest.
2. Get an external DVD burner that's faster than your existing one.
3. Get an external hard drive. You probably wouldn't be able to boot off it, but it would give you more space for data.
4. Get a nicer monitor. If you're going to stare at it all day, you might as well make it easier on the eyes.
5. Get better speakers. If you watch DVDs or anything on your computer, it might be worth it.
6. Get a joystick or other video game pad. If you play games this would come in handy.
7. Get a flatbed scanner. Scan your old pictures and your dental x-rays (if you're weird like I am).
8. Get a web cam. Let your distant loved ones see you.
9. Get a headset with microphone. If you want to make free phone calls on the internet, a headset with microphone will make it work a lot better.
10. Get a better printer. You might want to print out a photo once in a while.
Just go to a good store and see what will plug into USB, FireWire, serial, or parallel ports.