I'm not a fan of sports games at all but i absolutely loved
Everybody's Tennis!
Aside from the RPG elements the actual Tennis mechanics were pretty solid and even addicting.It was also one of the few games were the PSP's analogue button provided really good control over character movement. I spend countless of hours on this gem but surprisingly never beat it (my PSP save file got corrupted and lost all my progress). I really want to replay it one day though.
As for racing games
Modnation Racers on PS3 will always be one of my favorite Kart racers ever (can't say i've played too many though
![Stick out tongue :p :p](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
)
Really what i can say about this game! Excellent handling (the drift was sooo satisfying),incredible track design by United Front Games (RIP) and the game was just pure fun! Another game that i have put a crazy amount of time on it especially playing tournaments with friends with its couch split screen multiplayer.
The only sad thing about it is that the servers got closed down and some fantastic creations from its very talented (and i really do mean VERY talented) community got lost forever.
I'd also suggest:
Horizon Chase Turbo (that was a very pleasant surprise and really loved it).
Initial D Extreme Stage (although if you don't know Japanese the game gets very hard since you have to know how to tune the car for each race).
Auto Modelista (i haven't put much time into it but the game is worth it just for how beautiful and unique it still looks).