I recently got a PS4 and I was wondering if I could play games like GTA:V with my PS3 friends? I'm thinking that you can't but wanted to confirm. I tried playing with them but it says that they aren't playing GTA:V.
No to GTA V.
There is no official statement about this, but Rockstar never announced to be working on any form of crossplay feature for GTA V afaik.
However, there are games that do offer online crossplay between the PS3 and the PS4, see this wikipedia page.