Listed in timeline order.
1. N64
2. PS2 (only for FFX)
3. Xbox 360
The original Xbox also places a soft spot on me due to KOTOR and SW: Jedi Academy. I love those games! But for the sake of the OP, I'll keep it to my numbered top three.
Everyone needs to play Lost Odyssey! Any opposition to this and I will have to just say, "If it's a fight you want, you got it!"