Sony's relationship with backwards compatibility has always been best described as "transitory towards breakup" (c.f. PS2 discs in a PS3). So far, however, the progenitor PlayStation games, as disc and as downloads, have continued to enjoy legacy support in all hardware. That streak ends with the PlayStation Vita. According to Sony's official Vita FAQ, the "Game Archives" — which includes both PS One and TurboGrafx-16 titles downloadable from the online store — will not be supported at launch
Like we said, backwards compatibility has for awhile been a sore spot for Sony consoles. The PlayStation 3 went from fully supporting PS2 discs to partially supporting them (pretty much all models before 2007) and now doesn't support it at all aside from tweaked "remakes" available for repurchase through the online PSN store. Sony says additional announcements on Archives will be made shortly, so we're pulling for this being an impermanent situation. With any luck, it'll all be resolved by the time Vita launches outside of Japan sometime next year.