I've got a Canon 5-something-or-other that I bought through our classifieds here on the site. It's got very effective auto-focus and zoom (though the zoom tends to drain the batteries very quickly) and I've had luck with it at a much wider range of distances than I expected, from very close-up flower pictures to landscapes. It also does short videos, though I haven't tried that feature so I can't speak to its quality. All the photos I've posted in this forum and in my livejournal photo gallery were taken with it. Not all the photos in my portfolio at
http://www.crysodenkirk.com/gallery.php were, but all of the most recent pics were. It's got a much better picture quality than you would normally expect from a smaller camera.
I haven't used any of the low-end Olympus cameras in several years, but I know at the time they were not nearly as good as their competitors of the same price.