I feel like many consoles had some great elements to them, it would almost be easier to list ones that did nothing.

For me, I have like three that come to mind for consoles and then maybe two for handhelds.

For consoles:

The SNES and PlayStation were both pretty sweet consoles with some of history's greatest games on it, but more importantly, I feel like these two systems saw the biggest strides in technology for the medium. With the SNES/Genesis, we got to see the gap between home console and arcade get closed in and many sub-genres began to really take root in this era. It was also the last gen where I felt Nintendo was truly king of the gaming hill. The PlayStation was simply when the gap disappeared almost entirely between arcade quality and home version and we saw several genres really transform and the medium mature. Companies like Square and Konami were in a Golden Age by this time, and we finally saw the massive Japanese gaming market open up in the West, while western developers really started to step up their game to compete. I also consider these eras to be the last time the console wars were actually "fun and good nature" before all of us grew up to be pricks about it with consoles that didn't deserve the attention.

My third choice is the PlayStation 2, which largely benefited from the advancements made from the previous two gens. While the previous two gens were largely more groundbreaking in terms of technology and theory, the PS2 beats them both out by have the largest and possibly best collection of titles at it's disposal. The PS2 library is so large, I can't imagine someone couldn't find at least one great game to play on it. So it's largely here for having a stellar gaming library, and that's even before talking about backwards compatibility and ports.

For handhelds, I'll give it to the GameBoy for starting it all in terms of making a portable game system with interchangeable games something viable and away from simple Tiger Handheld titles. Super Mario Land, Final Fantasy Legend, Link's Awakening, and of course Pokemon all really help make this handheld standout.

My second choice is probably the DS for having a pretty gimmicky premise but actually making it really work. Not to mention it also had a pretty sound gaming library which was made better with the backwards compatibility of the underappreciated GBA.