While putting together, I realized Pentax didn't have one in its lineup--budget or otherwise. However, as of Wednesday, it does: the Optio RZ10.
Priced at a reasonable $219.95, the 14-megapixel RZ10 features a 10x f3.2-5.9 28-280mm-equivalent lens with sensor-shift image stabilization and a 2.7-inch, 230K-dot resolution LCD. It can do macro shots as close as 0.4 inch from your subject, has a 720p HD-resolution movie mode, and a burst-shooting option that can capture up to 40 photos at up to 9.1 frames per second (though that's likely not at full resolution).
If those features were all it offered, that would put it on par with other cameras in its class. To make it a little more interesting Pentax adds support for Eye-Fi wireless SD/SDHC cards, some digital art filters (including Toy Camera and Retro), smile and blink detection, and improved dog and cat face detection. The last one may seem silly, but people take a lot of pictures of their pets and it does help make sure they're in focus.
It'll be available in October in black, white, lime, and violet.