While some people may have been holding out hope to play PS2 and PS3 games on their PS Vita down the line, Sony have put an end to the speculation in their PS Vita FAQ over at the official blog.
"Users can play supported digital PSP titles and supported minis. In regard to PSone classics titles, we will announce further details when they are ready. PlayStation does not have plans to make PS Vita compatible with PS3 or PS2 titles at this point."
Of course, there will be some cross platform titles on Vita and PS3 that only applies to specific titles, such as Hustle Kings, and bought DLC will work with both versions of certain games such as Ultimate Marvel vs Capcom 3.