I bought a few accessories that have really enhanced my experience with my Powershot SX20 IS:
1. Rechargeable batteries: Although the SX20 is pretty economical with batteries, having a couple of rechargeable sets mean that I don't, in theory, ever have to buy any more batteries for it. I went in for the Canon CBK4-300 Rechargeable Battery and Charger Kit, which costs a bit more than other models, but decided to go for the Canon name brand. I haven't regretted it - they have great battery life, and I took hundreds of pictures on a single charge.
2. Lens cap holder: One of the few annoying features about the SX20 is the fact that the there is no convenient place to keep the lens cap when you're shooting. It gets to be a pain to hold on to it, so I spent a couple of dollars to buy a lens cap holder that attached to the lens cap and tethers it to the body of the camera. Definitely a good investment.
3. SDHC memory cards (8 and 16 GB): I bought Transcend SDHC memory cards, one for backup. Although the 16 GB card holds about 6000 photos and I'm not about to fill it up any time soon, I think it's a good idea to keep a backup card in my camera bag just in case the main one gets damaged.
4. Gorillapod (tripod): Since I would like to practice some serious photography with the SX20 IS, I thought it would be good to invest in a small tripod. The Gorillapod SLR is a flexible, lightweight and relatively inexpensive tripod that works well with small SLR and prosumer cameras. If you get one, make sure to get the Gorillapod for SLRs, as a smaller one might not hold the weight of the SX20.