There are many such moments for me really.
On the hardware front, roughly in chronological order...
1) The day I first saw an amiga. I was a schoolkid and one of my friends dad had just got an A1500. It was something else.
2) The day I got my first amiga. I had lost interest in the whole computer scene over my teenage years (on reflection a good thing really), but when I was 18, I got nostalgic and was after a computer. To my delight, my mum got me an A600 for my birthday plus some magazines with coverdisks (introducing me to Protracker and Octamed).
3) The day I got my first A1200. This was xmas the same year as the A600. I'd learned by then that the 1200 was a much more expandible route to take. I still have the A600 but alas it is not working :-(
4) The day I shoved a hard drive in it :-) It was 1.28GB in the days when PC's typically shipped with 500MB :evilgrin:
5) The day I got my first accelerator. Having saved for the B1230-IV with FPU, the apollo 1240 appeared on the scene and I opted for that instead. The increase in performance over the base A1200 was jaw dropping (especially once I installed some patches to move all the system stuff to fast ram).
6) The day I got my BPPC and built my 1200T. I wanted to get the 060 version but at that time it was way too expensive. However, I reasoned that PPC should open some interesting possibilities. I wasn't dissapointed :-)
7) The day I got my first RTG card, the BVisionPPC and a 19 inch display to go with it. The difference from AGA was incredible. No more 1280x1024 (autoscrolling 640x512) 16-colour laced workbench with magic tv, now I could enjoy 1600x1200x16-bit colour at 75Hz.
On the software front, each new release of the OS. I started at 2.05 and worked my way up through each major version since, although I still use a 3.5 installation for most of usage.
Demos. Where do you start? Each new one you saw just left your jaw swinging.
There was OctaMED, which evolved into the bear-perfect tracker (IMHO). Each new version was a delight :-)
Art packages - from DeluxePaint II and on. DPaintIV AGA was a lot of fun :-)
Games - too many to mention, really but Turrican, Syndicate, the Alien Breed series and later the 'impossible', Doom, quake etc.
The day I wrote my first working C program on the amiga.
Damn, that's like too many memorable moments. Do I have to pick just one?