Uhm. This is stupid. "consoles?" 

You don't play a console. You play games.

Well I dont like the whole "true gamer" crap but these are the three im fondest off I guess

SNES

DS

Sega Gen.

Im actually really found of other systems too I just think overall these had the best games (which is themost important part of any console) and have gotten more than their far share of my playtime.

Xbox 360

PS3

(insert random opinion console)

1. SNES

2. DS

3. Gamecube

4. (To not sound bias): PS2

N64 

SNES

Zeebo 

You can't limit it to just 3.  You can't even fit all the 'must play' Nintendo consoles in 3 choices.

That said:

1. NES - If you want to play one of the biggest and most influential libraries in the history of gaming, you need to have played the NES.

2. PS2 - Same as NES.

3. 3DS - In theory, you'll be able to play the entire lineup of Game Boy, GBC, GBA and DS on this one system.  And you can't ask for a more amazing thing than that.

FAIL!

If you're a true gamer, you play on any console.

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.

How could I forget about that masterpiece!