The PS4 is rumored to be getting PS1 and PS2 game compatibility with native 1080p rendering for "select titles". The information is from a few recent GDC tweets posted below.
Be excited:
1. Local PS2 / PS1 support on PS4 w/ native 1080p rendering for select titles.
2. Bluray+Media Player updates
— Ahsan Rasheed (@thuway) March 25, 2014
@reptilescorpio Number 1 I've known for a good minute, but software is still buggy and not every game works. Please be excited.
— Ahsan Rasheed (@thuway) March 25, 2014