+ PlayStation 4
- SNES
- NES

23 - PlayStation
23 - PlayStation 2
22- Super Nintendo (SNES)
19 - Nintendo Entertainment System (NES)
14 - Nintendo 64
13 - Nintendo 3DS
13 - Nintendo Switch
12 - PlayStation 4
11 - GameCube
11 - Nintendo DS
11 - Dreamcast
7 - Sega Genesis
6 - PlayStation 3
5 - PlayStation Portable
3 - Game Boy Advance

ELIMINATED:
1) Phillips CD-i
2) Nokia N-Gage
3) Game.Com
4) Action Max
5) Wonderswan
6) Atari 5200
7) Virtual Boy
8) 3DO
9) Magnavox Odyssey
10) Atari Jaguar
11) Xbox
12) Atari Lynx
13) Sega Nomad
14) Xbox 360
15) Sega 32x
16) Xbox One
17) Atari 7800
18) Neo Geo CD
19) Wii U
20) Magnavox Odyssey2
21) ColecoVision
22) Intellivision
23) Game Gear
24) PlayStation Vita
25) Neo Geo
26) TurboGrafx-16
27) Sega Master System
28) Sega Saturn
29) Atari 2600
30) GameBoy/GameBoy Color
31) Wii

+ Gameboy Advance
- PS4
- PS3

23 - PlayStation
23 - PlayStation 2
22- Super Nintendo (SNES)
19 - Nintendo Entertainment System (NES)
14 - Nintendo 64
13 - Nintendo 3DS
13 - Nintendo Switch
12 - PlayStation 4
11 - GameCube
11 - Nintendo DS
11 - Dreamcast
11 - PlayStation 4
7 - Sega Genesis
5 - PlayStation Portable
5 - PlayStation 3
4 - Game Boy Advance

ELIMINATED:
1) Phillips CD-i
2) Nokia N-Gage
3) Game.Com
4) Action Max
5) Wonderswan
6) Atari 5200
7) Virtual Boy
8) 3DO
9) Magnavox Odyssey
10) Atari Jaguar
11) Xbox
12) Atari Lynx
13) Sega Nomad
14) Xbox 360
15) Sega 32x
16) Xbox One
17) Atari 7800
18) Neo Geo CD
19) Wii U
20) Magnavox Odyssey2
21) ColecoVision
22) Intellivision
23) Game Gear
24) PlayStation Vita
25) Neo Geo
26) TurboGrafx-16
27) Sega Master System
28) Sega Saturn
29) Atari 2600
30) GameBoy/GameBoy Color
31) Wii

+ PS3
- Sega Genesis
- Gameboy Advance

23 - PlayStation
23 - PlayStation 2
22- Super Nintendo (SNES)
19 - Nintendo Entertainment System (NES)
14 - Nintendo 64
13 - Nintendo 3DS
13 - Nintendo Switch
12 - PlayStation 4
11 - GameCube
11 - Nintendo DS
11 - Dreamcast
11 - PlayStation 4
6- Sega Genesis
6- PlayStation 3
5 - PlayStation Portable
3- Game Boy Advance

ELIMINATED:
1) Phillips CD-i
2) Nokia N-Gage
3) Game.Com
4) Action Max
5) Wonderswan
6) Atari 5200
7) Virtual Boy
8) 3DO
9) Magnavox Odyssey
10) Atari Jaguar
11) Xbox
12) Atari Lynx
13) Sega Nomad
14) Xbox 360
15) Sega 32x
16) Xbox One
17) Atari 7800
18) Neo Geo CD
19) Wii U
20) Magnavox Odyssey2
21) ColecoVision
22) Intellivision
23) Game Gear
24) PlayStation Vita
25) Neo Geo
26) TurboGrafx-16
27) Sega Master System
28) Sega Saturn
29) Atari 2600
30) GameBoy/GameBoy Color
31) Wii

The NES saved video gaming in North America.  The NES had an at retail 20 year lifespan.  The NES saw the birth of Super Mario Bros, The Legend of Zelda, Metroid, Castlevania, Final Fantasy, Dragon Warrior (Dragon Quest), Ninja Gaiden, Mike Tyson's Punch-Out!!….  

"In 2009, the Nintendo Entertainment System was named the single greatest video game console in history by IGN, in a list of 25."

"The NPD Group today released its report for April 2017,...Another interesting thing to note is that the NES Classic was the No. 2 best-seller in the US during April, outperforming Xbox One and PS4"

Sorry, the 4 1/2 year old PS4 doesn't hold a candle to that legacy.  

I feel the urge to point out that this voting game is not only about legacy.

Otherwise the Odyssey for example would be somewhere else in this list...

PS4 is probably better than 64 and GC, even considering each one in its epoch and context, and it's still better than NS, that still has to show its full potential, but NES in its era accomplished probably the second biggest goal ever in console gaming: after Atari 2600 (that shouldn't have been eliminated so early in this little contest of ours) truly launched the market, NES resurrected it after its first crisis, probably its worst ever, had left it almost dead.
Switch is still on the right path, and growing, to save, at least for another gen, portables from mobiles, it looks it can do it better than 3DS.
PS4 is becoming huge, it's thriving, but it's doing it starting on the shoulders of a previous excellent generation for home consoles, when even the losers enjoyed excellent sales, so its achievements, huge in absolute, are less impressive comparatively.

Edit. PS: But the contest rules clearly let voters use their favoured criteria, so deal with it. BTW I upvoted PS4 too feeling it deserves a better ranking than other machines, and I feel NS and DS should be above 3DS too, but I wouldn't do it compared to NES.

If that's your reasoning, then I urge you to reconsider as we are voting on best, not "most important". 

+PS4
-N64
-GameCube

23 - PlayStation
23 - PlayStation 2
22- Super Nintendo (SNES)
19 - Nintendo Entertainment System (NES)
13 - PlayStation 4
13 - Nintendo 64
13 - Nintendo 3DS
13 - Nintendo Switch
11 - Nintendo DS
11 - Dreamcast
10 - GameCube
6- Sega Genesis
6- PlayStation 3
5 - PlayStation Portable
3- Game Boy Advance

ELIMINATED:
1) Phillips CD-i
2) Nokia N-Gage
3) Game.Com
4) Action Max
5) Wonderswan
6) Atari 5200
7) Virtual Boy
8) 3DO
9) Magnavox Odyssey
10) Atari Jaguar
11) Xbox
12) Atari Lynx
13) Sega Nomad
14) Xbox 360
15) Sega 32x
16) Xbox One
17) Atari 7800
18) Neo Geo CD
19) Wii U
20) Magnavox Odyssey2
21) ColecoVision
22) Intellivision
23) Game Gear
24) PlayStation Vita
25) Neo Geo
26) TurboGrafx-16
27) Sega Master System
28) Sega Saturn
29) Atari 2600
30) GameBoy/GameBoy Color
31) Wii

While you answered me, I edited my post to add that the contest creator clearly let each voter use their favoured personal criteria for "best".

Just remember that the most powerful doesnt mean its the best console. The best console is the one you´ve enjoyed the most time one or is the most important to you.