The period of time begining the release of the Sega Saturn in 1995. Right now (2000), with the release of the Sega Dreamcast and Sony PlayStation 2, the 128-bit era is dawning, and 32-bit is coming to a close. The machines of this period are the Sony PlayStation, Sega Saturn, and Nintendo64 (a 64-bit system, but put in with this time period). Consoles of this period are also referred to as "Next Generation" because of the long transition period before the 32-bit era, with people always looking towards the next big thing. This era also saw Sony emerge as a major player in the console market, having previously only played a bit part; and Sega and Nintendo, the two giants, being beaten at their own game. It is a fact that no console manufacturer has succeeded in holding a market lead from one generation to the next. Sony appears to have succeeded in breaking this trend however, as their victory in terms of sales with the PS2 seems assured. Consoles of the transition era are generally given their own classification, since they mostly did not last long past 1995, and mostly did not achieve mass market success.

Update (19-Aug-2004): I should add that this naming is really just a convention, and I'm well aware that "128-bit" doesn't accurately describe the current games consoles on sale. But it's the phraseology in common usage and that's what I'm documenting. No-one talks about the Xbox et al as 32-bit, despite the nature of their processors. It allows the distinction to be made in people's minds.