Benny's speech. Then the gunshot that leads into some heavy western twangy-ness. Just epic.
QFT. The whole opening cutscene sets the tone of the game extremely well, but that moment in particular always sends chills down my spine.
My favourite part of the game though? That stretch of the game right before you enter the Strip and really dive into the main quest. At that point I usually have decent equipment and skills, with ED-E and either Boone or Veronica. And at that point it still feels sort of personal, once you start with the main quest it feels like you're being swept up in the big picture. Which is very cool, but also has a very different flavour to what came before.
That's generally, in every game. On my first playthrough there were a few quests that made me go FUUUUU- ZOMG - the climixes of 'I Could Make You Care' and 'Return to Sender' in particular.