What? Show me a host offering even p3 servers for under 20 dollars a month.
Not a P3, but you occasionally see P2s offered that cheap. http://www.lowcostdedi.co.uk/ is the only one I can think of off the top of my head (I have one of there cheapest, no complaints so far though I've not had reason to really test the network speed or support yet), but there have been others in the offers forums.
You shoulodn't expect a lot from such a server, but they do a good job of being DNS servers and such. And I'd wager that for some use cases they'd outperform a similarly priced VPS.
You do sometimes see P3s at the 25..30 mark, as has already been pointed out, so it may only be a metter of time...