It's funny, when I think back it's definitely the N64 as I adored that console and was so hyped playing Mario 64, Starfox and the two Zeldas.
But it could also be the Gamecube for me. I have fond memories playing Mario Sunshine when I was ill and stayed home for a week.
The PSP was also amazing. I got a PSP Go late in the console's life cycle for 99€ with 10 free games. Couldn't believe how many cheap AAA games there were on the Playstation Store: Ratchet and Clank, Jak & Daxter, God of War... the games all cost 7.99€ a pop, it was insanity.
So in terms of impact the N64, in terms of memories the Gamecube and in terms of value the PSP.