Playstation 3 has earlier been reported having some problems with backwards compatibility. This has mainly applied to Playstation 2 since this hardware is a lot more advanced than the first Playstation console, but unfortunately they are both causing problems. It turns out despite that the console was launched, and that Sony had promised that the compatibility would not be a problem, that all too few games are working satisfactory or even at all. Sony has been working and is still working on fixing this through both firmware and software updates.
This will hopefully be less of a problem when the consoles arrives here in Europe, but until then you can visit Playstation.com and check how the old games work together with med Playstation 3.