I have a few games that I want to bring to PS4 when I get one. It's Destiny, Advanced Warfare, and other digital games that are also on PS4. So if its on ps4 and I have it on my ps3, can I download it again?
It depends on the developer and publisher of the game. If the game employs the
cross-buy system, a PS4 license should automatically be added to your account when it is released, if you purchased the digital version of the game on the PS3.
This was the case with the recently released PS4 version of Journey, as well as with Flower, Spelunky HD, The Unfinished Swan and several other games.
You can confirm whether a released PS4 game supports cross-buy simply by visiting its store page in the PSN store. If you bought the game on PS3 and it supports cross-buy, instead of a Buy button with a price tag, there should be a Download button or Options button, which offers alternate download options in a drop-down menu.