Can I play the PS3 games I play online, online with the Vita?
Do you mean multiplayer between the PS3 and PSVita? Or do you mean 'remote play' by using the PSVita as a screen and control of your PS3 over the internet like Sony tried with the PSP?
Because 'remote play' is available for developers to use if they want, so you will have to wait to see if your game is supported.
And withe the first option you that will also have to wait to see if the developer creates a PSVita versionof the game that is multiplayer compatible. We know thta "Ruin" and "Hustle Kings" will be PSVita releases that can also play with the PS3 versions, and WipeOut 2048 will allow the tracks that are in common with WipeOut HD to be played PSVita to PS3.