For PVP:

Absolutely wrecking my younger brother in One Must Fall 2097 back in the early aughts.

We also used to play Need For Speed High Stakes and would challenge each other to beat our best track times. I routinely trounced him in the McLaren F1 GTR while he was a shill for the Mercedes CLK GTR.

For Single Player:

Mission 11 in Project Wingman. The huge dogfight and that soundtrack just clicked in me.