Hopefully fixed my images...
Here are a few:
When I first managed to do this in Galaga:

Gyruss: It was just a fun experience.

Quartet: I don't know if this was the first 4 player game, but it was one that I most remember playing. (I think there were a few driving games like sprint that had 3 or more driving wheels).

Walking into an arcade and hearing screams of pain. When I finally get to the head of the cue to see what game it was I saw this:

(Golden Axe)
The next few are sound related:
I have spent lots of time listening to the music at these title screens on my C64:

and

Ahh... Ahhh Turbo Outrun and R-Type.
Then on my Amiga when I first got it...
I had setup speakers behind me close to where my head would rest when I'd sit down to play. I got my first taste of cool music with this game...

Then came the clear voice in this game:

That awed me at first.
The game that sold me on the SNES:

Especially at that point where you're diving down to the planet and about to play the side scrolling section. That whole segment gave me goosebumps!
The big distinctive moment for turbo gaming for me came from this area of Dracula X:

When I first played Dracula X, I was so hyped that at the start of the game I felt a little disappointed. It was at the moment when I entered the castle, and the music played an all too familiar tune and the graphics really stood out for its time.