Ideal lens for Canon 40D for landscape photography under $600?

Bryan, neither the 24mm nor the 28mm will be very wide on your 40D, with its 1.6x crop factor. It appears to be the consensus amongst crop body users (of which I am not one) that the best wide angle for landscapes is the EF-S 10-22mm zoom, and it's only a little over your budget (link).

Landscape tends to be more suited to wide to normal perspective. Only occasionally will a telephoto serve well. In your price range I'd consider the Canon 17-85 EF-s. Do you have the 18-55 kit lens? That's actually a good landscape range.

It depends on the style you are after. Telephoto lenses are more typically used for only certain types of shots, such as a zoomed in shot making the sun look larger against a distant scene. Landscapes usually utilize wider angles to incorporate more of the surrounding scene. Right here on photo.net, look up the works of Marc Adamus , Camilo Margeli , Tomas Casper , Chip Phillips , and many many more landscape photographers. They typically use wide angle lenses such as the 17-40L or 16-35L lenses.

Now, since you use a cropped sensor camera, you may be interested in getting a wider lens such as the Canon EF-S 10-22 which would give you about the same field of view as the 16-35 on a full-frame camera like the 5D. I started with an XTi (400D) and a 10-22 and eventually moved to a 5D and 17-40. I like wide, that is my taste. But be sure you like this style though before you invest in wide angle lenses, it could be that you prefer more normal focal lengths.

If you decide to go wide, these lenses should be considered:
Canon EF-S 10-22, (only for cropped sensor cameras) about $700 link
Or consider the Sigma 10-20, (only for cropped sensor cameras) about $480 link
For more zoom although not nearly as wide, the Canon 28-135 IS, about $400 link
Canon 17-40L, about $730, link

Also, keep in mind that these can all be picked up used for less money at places like fredmiranda.com, adorama.com, keh.com, and even ebay.com if you dare shop there, haha. Fredmiranda.com is a good place to read user reviews of lenses as well.
I'm sure there will be some other good recommendations in the following posts as well. Happy shopping! Think long and hard before you purchase.

I picked up the Tokina 11-16mm f/2.8 lens and I couldn't be happier with it. Incredibly sharp and great contrast. Not much zoom range but that's never been an issue for me. It comes in just under $600, but it seems a little tricky to find stock anywhere these days.
(link)

I really like my Sigma 10-20mm. It's great for the wide angle on the APS-C bodies. However, "landscape" can be taken with any focal length, depending on what you are trying to do.

I guess you could call the picture below a "landscape," but it was taken with a Reflex-Nikkor 500mm f/8 lens on a Canon 20D.

The point is that not all landscapes need more than a regular complement of lenses.

The tokina 11-16 is highly regarded.

I have the Tamron 17-50 2.8. It is a very nice lens! Very sharp! Very usable range! B&H Photo has the for $460. It is worth the price. Check my portfolio, alot of the picture in it are taken with this lens mounted on a 30d.

I would get a wide angle for landscape. The 10-22mm is a great lens and the widest angle available on a 40D, however I found it was too wide for most situations and had no reach so I sold it. I bought a 17-40mm f/4L that gives me a little more reach and if I need super wide then I stitch. Stitching gives you a higher res image that is capable of larger prints so this worked out best for me anyways. There are other wide lenses to consider too, but I would get something that is 17mm or less on the wide end; and don't get a fisheye.

It depends on the type of landscape photographs style you want to take. When travelling in the Himalayas with a film camera I rarely wanted wider than my 28mm lens so I find my 17-55 (or 17-40) are great for landscapes as these give the same field of view at the short end. At the moment I am not sure I would spend the money on a 10-22 (which is a very good landscape lens) for the few times that I would use it.
Also, the 10-22 demands much more care in composition or you risk taking a lot of mediocre pictures, compared with using more 'normal' focal lengths.
I agree with JDM - you can take a landscape with any lens and I use my 70-300 as much as I use the 17-55.

What lens do you have at the moment? I am presuming it is 18-55 (or similar) so the question is do you want wider, or do you want better quality in the range you already have?