If you don't want to run full up Linux you can do this with the ST Micro STM4F32, its Cortex-M4 chip with ethernet capability. At about the same price (in small quantities) you can use the Atmel SAM9 series, just chip, memory, ethernet MAC, and USB is about $25 in parts (single unit quantity) so if you made a bunch your cost would be closer to $15 but if you sell them you need to make some sort of profit to cover the cost of building them.

Close though, and I suspect we'll see SOC's that target this market soon enough. One workaround is a development environment that lets you compile a Linux application into something that can run on the hardware (just the kernel you need, and nothing extra :-) The uC Linux work is interesting in this regard.