I'm considering trading in my PS3 toward a PS4 and I have a bunch of PSN games on my PS3:Shank,Shank 2,Mortal Kombat II,Sonic Adventure,Assassin's Creed Freedom Cry etc.Does the PSN store on the PS4 have these same type of games on it or since all my PSN games are tied to my account on my PS3 will I just be able to re-download them onto the PS4?If neither is the case,does that mean I have to keep my PS3 in order to play these and all my other PSN games?

None of your PSN games transfer unless they are specifically stated to be crossbuy or have a digital upgrade like Guacamelee.

Aw :( oh well.

Currently no, but its possible that PS Now will let you play those at some point.

The PS4 is not backwards compatible with PS3 games, whether they're on a disc or digitally downloaded, a PS3 game is a PS3 game and the PS4 doesn't play them. With that said, as @corruptedevil pointed out there are many games on the Playstation family of systems that are available on two or even all three current Playstation systems (PS3, PS4, Vita), many of which are cross buy. If you do happen to have any cross buy games on your account you will be able to download them on your PS4 with no extra purchase.

Here is a list of all the cross buy games and what system they are available on: PSN Store Page

If you're still gaming on your PS3 and don't have much interest in sports games like MLB The Show or NBA 2K I'd suggest holding off a little longer. Most of the best stuff on PS4 is local multiplayer (Sportsfriends, Towerfall) or more novelty than full product (Doki Doki Universe, Ground Zeroes). It's fascinating system but it doesn't have as much functionality as a PS3 (for example, without a regular analog audio out there's no easy way to hook it up to regular speakers, it doesn't have the HBO or Youtube apps yet, and you can't stream media from your local PC to the system - it's a substantially less all-around device than the PS3 is)

Also, when you really look at it a lot of its best games - Assassin's Creed IV, Battlefield 4, CoD: Ghosts (my friends seem to be playing this all the time), Fez, Final Fantasy XIV, Flower, Injustice, Rayman Legends, Tomb Raider, Trials, Watch Dogs, and Wolfenstein to name the ones I think look fun or know are fun - are available on the console you already own. They look prettier but that's about it.

However, if you just want to sit in awe in front of your TV screen for a day or two, grab that PS4 with copies of inFamous and Ground Zeroes and show all your friends how much cooler you are now. Sometimes all it takes is graphics; I convinced a friend to buy a PS4 after he came over to play MLB 14 a month ago, he just couldn't help himself. He had to be seeing graphics that crisp at home.

Don't trade in you ps3. The 80 bucks you'll get for it (assuming you go through gamestop) isn't worth losing access to the games you already own/the catalog of available games on the platform. And I don't really have any faith in sony to make ps now that useful of a service where they'll let you stream games you already own for free (or with ps plus). I love playstation, but I don't think they are smart enough to do that. It's gonna end up being a service where you either pay a huge subscription fee or pay egregious rental prices on a per game basis.