If you want a cheap lens that is wide on an APS-C DSLR, you've got a serious problem because the crop factor makes you want a very short focal length and avoiding the mirror forces the back of the lens to be too far from the sensor (more than ~40mm). Thus, we're talking retrofocus lenses, and it wouldn't be far off to think of one such lens as a simple wide angle lens packaged with a second lens to reproject the image behind it. There are about twice as many elements as in a longer focal length lens. Zooms complicate the design further, and the fact that people love zooms has made tele-biased zooms the dominant market.
Options for that wide-angle look on APS-C:
(1) Redefine $500 to be cheap and buy the Sigma 10-20. I use mine at 10mm more than 90% of the time. It's great when stopped down to f/8, but very soft wide open. There are a few fixed focal length or zoom competitors for this lens, but I have yet to find one as cheap that equals it. Incidentally, part of why this lens works is that it doesn't have to cover full frame, just APS-C.
(2) Get used to cropped wideness. For example, my M42 35mm f/3.5 SMC Takumar definitely has the depth of focus and colors of a classic moderate wide landscape lens. Even though an APS-C sensor doesn't capture a wide angle of view using this 35mm lens, it still captures landscapes just as beautifully and with the same "look." Of course, it is problematic when you can't step back any further to fit things in....
(3) Hunt down an old rectilinear lens in the 17mm-25mm range. There are plenty; I have a Spiratone 18mm, Vivitar 20mm, and Tamron 24mm. Catch is, they're not great IQ and pricing is going nuts: often well over $100, and don't even think about the Flektogons on a budget. Generally, the design and construction is quite good, but the coatings aren't great, and with lots of elements that leads to low contrast and more potential for flare. Often, there's CA too (which the sensor and microlens array make worse than it was for film -- they don't handle light arriving at angles well). The good news is that most of those IQ issues can be helped in postprocessing, so final IQ might surpass that of a modern kit zoom.
(4) Use a distorting wide angle lens and digitally correct. Lenses with a little barrel distortion are easier to make (e.g., Panasonic's 14-140mm and 20mm) and perhaps we'll soon see lenses for other than 4/3 mount doing this deliberately to improve cost, size, and IQ. For now, cheap fisheye and supposedly non-fisheye wide-angle auxiliary lenses that screw on your lens like a filter often produce surprisingly decent image quality except for distortion and CA, which can be corrected in postprocessing. Just be careful about putting heavy auxiliary lenses on plastic-body kit lenses. There are also various prime fisheye lenses, with my personal favorite being the old Accura 12mm f/8 I got for about $65.
Personally, I favor option (1)... but (4) is your cheapest answer for getting really wide on APS-C, and it is viable. Actually, I do all four.