Yes, "Can it run Linux?" is a Slashdot meme that will not die. But when you're talking $100 to $200 toys with wireless networking built in, a useful operating system and some apps would be a Good Thing, no?
Run Sharp Zaurus apps on the $200
GP2X with Qtopia - Host USB too, so add your own modem, printer, keyboard, mouse, sound/MIDI interface etc
... or have a go at the
Nintendo DS version. Cheaper, smaller, somewhat more limited. Uses the Nano-X GUI, which no-one writes for by the look of it. OTOH, there's a library to run X11 binaries.
There's a bunch of others out there. The GP2X looks like the front runner.