While i was watching these videos past few minutes, they bring me many good memories, but i can't remember now any other intros, these were the first which "came to my mind" (didn't know how to write that, but i hope you understood) .
GP500, however I can't find a video of the intro. It was the most realistic bike sim at the time, and is probably still one of the hardest. Anyway the intro kicked ass.
Edit: just installed it, so I will capture the intro and upload it to youtube.
One of my personal favs was the intro to EOTB2. Turning the lights off, the sound (blaster) up, and settling in for a night of classic 2D D&D hack and slash was pretty hard to beat back then. If it was raining and thundering outside too, then all the better of course. The intro sets the tone perfectly.
What a ripoff! They just took the official intro to the actual aired MotoGP races. Okay it's the same franchise and they own the intro but they could've been a little creative for the game.
Though short, this was a nice video to watch when I bought the game a long time ago Grand Prix Legends -- The game that started my whole sim racing life