Generally MMOs and Free-To-Play games do not require a PlayStation Plus subscription to be able to play online. Games such as a Final Fantasy XIV: Realm Reborn, War Thunder, and Warframe do not require PlayStation Plus because they are either an MMO or Free-To-Play.
Also you are able to play the Destiny full game but it limits some features such as not being able to do raids, strike missions or the crucible and you can't invite anyone to your fire team either. This pretty much means without PlayStation Plus Destiny is a singleplayer game.
Obviously exceptions to this rule apply such as Watch_Dogs hacking missions but these features lean more towards a passive online experience integrated into the game and I doubt other online modes such as racing or PVP would be allowed without a subscription.
To put this in better context, games with online features that don't have a heavy focus on competitive/cooperative multi-player gameplay usually do not require a subscription unless it is an MMO or Free-To-Play game.
Edit: After searching the internet I am unable to find any list of PS4 games that do not require a PlayStation Plus subscription. It would seem that following the general rules listed above is the best way to gauge whether a game has free online play or not.