#3 - WipEout HD Fury (Kudos to Player2 for guessing this)
I've always had an incredibly soft spot for the WipEout series as it was one of the first games I played when I got my PS1; and I loved that Sony continued forward with it despite futuristic racers going incredibly out of style. HD Fury is absolutely the best entry in the franchise and hands down the best racing game I've ever played.
What made HD Fury great was variety. There's so much to do it's unreal. You have your standard, weapon-based races; time trials; detonator (a weird racing-shooting hybrid); eliminator (battle mode); zone battle (impossible to explain, tbh) and my favourite game mode of all time - zone (speed of your ship automatically increases; race without touching the walls).
Throw in some beautiful 1080p 60FPS gameplay; tonnes of ships and the majority of tracks from Pure and Pulse; a great online mode with a vibrant community and a campaign mode that will take you forever to ace, and you've got all the ingredients for a masterpiece. Honestly, it really pains me that Psygnosis shut their doors (not least because their office is about 15 minutes from my front door) but because they had become so talented at making this brand of racing game. I'll miss you, guys!