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I don't know what counts as *cheap*, but I'll put in a nomination for the Olympus AF-10 Super.
It's an Olympus, but I guess it doesn't get much attention since it doesn't have "stylus" or "mju" in its name. Seems to go for around $50-60 on eBay. I found mine at a thrift for under $10.
It's a chunky looking, but not massive camera. Powered by either 2xAAA or a 123 battery. And the shutter makes the most wonderful sound.
Takes nice pictures too.