Lunar Silver Star Story. Greatest PS1 game ever made. I only know about it because I came across it in a 2nd hand game shop where I live. I've replayed it several times now and I never get tired of it.
Super Sonic Acrobatic Rocket-Powered Battle Cars! (or SSARPBC for short)
Arguably the best party game available on the PlayStation Store but also great for solo play and online. Basically the concept is you are playing soccer in cars (that can sustain flight for a few seconds!). There are traditional fields like normal soccer fields, but there are also unique ones like a pirate ship and a circular field where the goals are back to back and you can drive through them. Also on all the fields you can drive on the walls and ceilings, great fun. Also included are a series of challenge mini-games (like playing with a block instead of a ball or playing goalie against a bunch of cannons).
There's trying to make a sequel but need more support. Come on people, what's not to understand? Soccer in cars, it's pure fun. There is a free demo on the store so no excuses not to try it out.
Disclaimer: I am not an employee or anything like that, just a very satisfied gamer!