Apart from Amiga, three other solutions:
Psion 5mx - instantly on/off, and a comprehensive word processor all ready to go (plus a whole lot more!)
Linux - roll your own. My Gentoo-derived system boots in about 15s.
Zeta/BeOS - much faster than OSX, Windows or standard Linux.
Another experiment: starting a highly optimised Linux from hibernation, with an image of the state of the system just after boot-up. I think that could be fast - EXTREMELY fast!