Uncharted
Great TPS games. The games get a lot of flack for being too linear, but you know what? I don't care. This is literally Indiana Jones in videogame form. Which Tomb Raider is too, but Uncharted refined the gameplay, graphics, sound, and everything else... Which then Tomb Raider (2013) took inspirations from the refinements of the Uncharted series. Basically, if you liked Indiana Jones, and you always wanted a videogame based on Indy, but don't like Uncharted, I think you're just being bias.
Kingdom Hearts
Love the games. I'm basically going to be repeating what other people find so awesome with these games, but I'll give you a warning on the franchise. If you're new to the series and will want to play KHIII, BUY THE OTHER GAMES! Say you only have a PS4 or Xbone, and want to play KHIII. Either build a PC to run emulations of the games, or buy a 3DS for DDD and a PS3 for KH1.5HDR and soon KH2.5HDR. I guess KH1, 2, and Re:CoM are straightforward enough, but KHIII will definitely have confusing stuff from DDD and BbS.
Final Fantasy
A lot of people are probably going to include this, so I guess I won't say anything more.
Yu-Gi-Oh!
I've never seen the entirety of any season, but I still love the anime and games. In fact, I'm still waiting for the Zexal 3DS game to be localized. It just came out last month in Japan, so I guess I still have a bit of waiting left. Also, can't wait for ARC-V!
There are way more franchises I like, but to list them all would require me to sit here all day long.