I've got a very-first-generation, USB-hobbled-by-polyfuses-until-I-performed-surgery-on-the-thing 256MB Raspberry Pi. The thing's part of my time-travelling Radio-4-Matic and thus transfers a few gigabytes a day over a little USB WiFi adaptor by streaming radio over the intertubes, buffering it for some hours then playing it back.
Uptime? Right now:
19:12:14 up 52 days, 15:46, 1 user, load average: 0.01, 0.09, 0.12
Last reboot was for a system upgrade of some description; the things are pretty stable now. (There have been many improvements to the firmware and system software.) My other Pi (a more recent 512MB model) is busy being a tiny home fileserver and virtual server backup device (remote stuff rsyncs over ssh to this thing) - I could easily use a spare PC for those tasks, but the result would be a lot less near-silent and much more power-hungry. Plus it can saturate 100Mbit ethernet with file serving - faster isn't much use when most of my stuff is on WiFi.
Make sure you've got a decent power supply. Apparently voltage drops can be a big source of instabilities. Power for my midget fileserver is via a Samsung cube phone charger; the radio's got a hacked-together DC-DC converter running off a mains-to-12V-DC adaptor. (I'm surprised the thing is as stable as it is, what with it solely relying on my impromptu electronics hackery!)