Welcome to the forum.
Because the 20D's sensor is smaller than 35 mm film, lenses that are usually made for the format of camera don't have as wide a field of view on the 20D. Therefore, I suggest something very wide...the EF-S lenses are a cheaper way of getting that wide view...the only downside is that EF-S lenses won't work on full frame Canon cameras...film or digital.
The regular kit lens (I've got one) is OK but not great. I'd suggest the EF-S 18-85 IS. It's wide end is 18mm which is fairly wide for everyday type of stuff....and it has Image Stabilization which allows you to get sharp shots with slower shutter speeds.
For another lens, that depends on what you want to shoot. You could go with a telephoto, something like a 70-300. 70-200 lenses are pretty good quality. There is an F4 version and an F2.8 version. The F2.8 version is very expensive and heavy though...but that would be an ideal sports lens. Sigma makes a good one too.
I would suggest a fast prime lens. The 50mm F1.8 is only $70 US...and because it's so cheap...every EOS owner should have one. Being able to use a lens with a maximum aperture of F1.8 is great when you need it.
You could look at an ultra wide lens. Canon makes a 10-22 or something like that. Sigma & Tokina (& Tamron I think) also have some ultra wide zooms. Good for landscape shots or big groups in tight spots. Try a search of the forum. There have been some recent threads about a wide lens for the 20D.
Did you know that there is a big camera convention this month...and that Canon is rumored to be introducing a replacement for the 20D? If that's true, you may want to hold out for the new model...will be in high demand though...or you may be able to get a good deal on the 20D if it's discontinued. It's still a great camera...I've got one.