I'd concur with the above advice.
Be aware that all UV filters are not created equal. Hoya for example makes standard, HMC and super HMC versions. The difference is in the multicoating on the filter. The more you pay, the better the filter. How much you need to pay depends on the quality of glass you're mounting it on. I would use HMC or super HMC on good canon glass. B+W also make good, slightly more expensive filters. Slim filters are available for wide angle lenses to prevevnt vignetting, but I would expect this not to be a problem due to the 10D's crop factor.
Check out
www.2filter.com for some useful information.
I'm interested to know re: the polariser comments above whether people have actually noticed the difference between the most expensive eg the B+W model mentioned, and the mid range filters eg multicoated Hoyas or standard B+W CPLs. Most of us would like to avoid paying more than we need to, and it's always interesting to know at which price point the law of diminishing returns starts to become important! Yes, you get what you pay for, but that doesn't always mean the most expensive option is the right one.
In terms of graduated neutral density, these are a must along with the two above filters. You use it to darken your skies to prevent loss of highlights. (You can try to work around this in photoshop with some success, but it is often better to shoot the photo properly in the first place!). I use Cokin filters. They are nasty, cheap plastic and generally considered to be rubbish! I'd advise using a TIFFEN or similar brand if you can afford it, but they're about $120. The Cokin is better than nothing.
I've enjoyed using an INFRARED filter on my canon digital rangefinders. I believe that the 10D isn't very sensitive for infrared, and therefore this filter wouldn't be very useful. Anyone have any exdperience? (This is certainly not an essential filter, BTW).
The other filter I'm considering for landscape/nature work is a Red Filter 25 or 29. This is meant to be useful for black and white landscapes, providing sky clarity/darkening that can't be fully emulated using photoshop. Once again, has anyone actually got experience using this type of filter for this application on the 10D?
Finally, the other filter which can be useful is a neutral density filter. This basically allows you to use a slower shutter speed, useful in nature photography for producing the cotton-candy effect on waterfalls.
Cheers,
Roberto