Lovely Planet, Super Puzzle Platformer Deluxe and Future Pinball (free game).

Euro Truck Simulator 2 - turn on your favorite radio station or album and drive around Europe, just mind wandering, thinking about nothing... Works every time :)

Earthworm Jim. There's nothing like some senseless platformer violence when you're feeling down!

Quake. Or Mortal Kombat. Just kill lots of enemies in a bloody way.

I hope so. Even if I didn't mind playing a FPS on a gamepad, I'm too cheap and stubborn to pay for online play, so I'd get nothing out of the console version unless I paid twice as much to get PS Plus on top of it.

Trine when I'm sick, the final level of Immortal Defense when I'm sad.

Yeah, the main reason I use PSPlus is because of Destiny.
I bought a yearly subscription which costs me €5 per month, so it's not a major expense for me.

There are some extra benefits, like getting "rented" games included in the cost, i.e. the 'monthly games'.
Sometimes there are some really good ones among them, like Just Cause 3 and Infamous Second Son. For me it has mainly been games I would not buy for myself, but that would be fun to at least play through once.

The main benefit though, for me personally, is the extra discount I get on games. For exmple they currently have a Ubisoft sale, where Far Cry Primal costs about €20, however I get the game at a discounted price of €16.

I tend to buy a fair number of smaller Indie titles that are PS4 or console exclusive, as well as larger PS4 titles that are exclusive, so the PSPlus discount actually does matter in the long run for me (personally), I end up saving more than what the cost is.

That's another thing I hate about PS Plus. I remember a couple of months ago Atelier Sophie was 30% off on Steam, and just 20% off on PS4, unless of course you had PS Plus, in which case it was 30%. I saw then that they weren't better discounts, they were the real discounts, that were being held ramsom behind a subscription.

For me, when I had my old systems before moving (now I only have my newly bought N64), was the Legend of Zelda games. I always feel like a kid again when I play them! (I only have Majora's Mask now, but if I see ports on the Switch I'll probably end up buying that next.)

Now days, though, I played Dragon Age: Inquisition on the PS4. Too many playthroughs than I care to admit! (But, I haven't played Witcher or Skyrim yet soooo that's probably going to change.)

Zeus for me.

Mindless games where you can just run around and kill stuff like Doom or Titan Quest.

Possibly it would be Pokemon for me. The atmosphere is very cheerful, there is combat but it's not really combat, and you can play for as long (or as "short") as you want: from just a couple random encounters or rematches to a really long session. Depending on the type of person you are, you might have established an emotional connection with your team, and they never fail you. In the world of Pokemon, hard work always has a reward: you get stronger, even if you lose the battle in the end, so next time it will be a bit easier.

For me it's quite different: while I DO love adventures (GOG only knows they occupy more than half of my GOG shelves), when I'm in a funk I simply can't muster the mental strength to solve their puzzles. (I think it's because I need to keep "storing" information about where and what objects are available to me so that I can combine them, but in this state whatever is keeping me down is always coming to my mind and interrupting my memory from commiting the game's information past the short term memory.)
I could, however, play a funny adventure I already completed like Day of the Tentacle, because in this case it's less about using my memory and more of reliving the game's story and dialogues. Much akin to rereading a good book.

Strategy games annoy me when I'm in this state. RPGs might work or not.... I'd be in a great state of mind if I needed to grind, not so much to follow a plot.
FPSs could work, if I were into them. Mindlessly shooting bad guys is bound to be an excellent way to keep your mind off bad stuff.

But what really works for me are open-world games (preferably action oriented). GTA Vice City and Arkham City both did a great job out of it in the past. Just go do whatever mission you want, or absolutely none of them... you're free to do as you like there.
Platformers also do a good job because they're usually action oriented as well. Someone suggested Mario games up above. I approve of their suggestion.