So now the PS4 is out... Does anyone know if PS4's and PS3's online multi-player is cross-platform?
For example, can someone playing COD:Ghosts on a PS3 play with someone on COD:Ghosts on a PS4?
It is possible for PS3/4 games to be Cross-Play but it is not the default. You will have to check whether each specific game supports PS3/4 cross play as it's up to the developer to implement.
Not at the moment. Maybe the CoD developers can add that feature after patching it, if enough users request it on CoD community.
Playstation.blog is your best source, considering it comes directly form playstation
Over here it states that the ability for ps3 and ps4 users to crossplay is available, but it depends on the developers.
Q: Can PS4 and PS3 users play together online, cross-platform?
A: The functionality is technically possible and some developers may choose to support it for their titles.
If you go on ps store you will see that there are downloads that allow you to play cross platform its under ps3/ps4
No, it isn't (for COD at least).