I find the thread title here misleading, if you wanted everyone's favorite consoles the thread title should of said Favorite Consoles and not Best Consoles. Judging which consoles are best is pretty easy based on sales alone but favorites are all up to the individual. (yeah I am being a bit of a stickler but whatever lol)

Doesn't seem fair to add my voice to generations I had no experience with so Ill skip the first couple of options.

Third Gen Game Console
Sega Master System

Fourth Gen Game Console
Sega Genesis/MegaDrive (Why split up Sega CD and 32X?)

Fifth Gen Game Console
Sony Playstation

Sixth Gen Game Console
Sony Playstation 2

Seventh Gen Game Console
Sony Playstation 3 (special mentions to the PSP and Nintendo DS)

How exactly was the Genesis "cool," let alone cooler than Nintendo?
Well their are several things:
-Underdog Factor against the largely dominate Nintendo
-Violent Games that Nintendo Largely shunned or heavily modified
-Blast Processing
-Streets of Rage
-Sonic = Mascot with a 90's in-your-face attitude
-It did what Nintendidn't

In all seriousness your not going to get a straight answer, its all totally subjective fanboy bullshit at this point. I will say as a child of the nineties it did feel "cooler" then Nintendo largely due to great add campaigns at that time period. None of it really matters now but back then if I had to pick a cooler console the Genesis would win hands down. lol