I'd also like to put in a secondary vote for the Wii U, which had a lot of great games, a few good RPGs, enhanced remakes of the awesome Gamecube Zeldas, and was honestly more fun than the PS4 or Xbox One in the early years of the 8th gen, started a few good franchises, plus Earthbound, but just didn't. That said, I'm glad the best games of the Wii U got second chances on the Switch, like Mario Kart 8 Deluxe, Tokyo Mirage Sessions and Bayonetta 2, and did all right, or in the case of MK8, did spectacularly. The Wii U could be said to have been a warm-up for the Switch.

And one other underrated system I'd like to recognize is... the Switch. Yes, I know its sales are currently in beast mode, so how can it possibly be underrated? Since it's less powerful, a lot of games skip it. Honestly, though, the games that tend to miss the Switch are the same games I don't care to buy on PS4 either, and most of the games I would have bought on PS4, like Valkyria Chronicles 4, Dragon Quest XI and Witcher 3, did end up on the Switch, and I chose to support the Switch by buying them for that platform. I even bought Mortal Kombat 11, Samurai Shodown, Doom and The Outer Worlds on Switch though Outer Worlds is a bit of a mess. So it gets dumped on by a lot of people for those reasons. It's my favorite system of all time at this point, and there's still more to come. 

GameCube for me. It had all the Nintendo IPs you wanted in F-Zero, Star Fox, Metroid Prime, Pikmin and Luigis Mansion. Some of those IPs havnt been seen since.
GameCube also had an amazing controller and dished out amazing visuals in such a small package.

Ps3, despite it's high cost and issues at the start, it took over the world and had so many great games with new ip's.

I'm gonna say Wii U. It had great exclusives as we know, but what other console has given you access to most of the Zelda catalogue, 2 of them being excellent remasters.

First consoles that come to mind for me are the Saturn, Dreamcast, Gamecube or Wii U (basically anything that isn't PS or Xbox) but I'm going to say the Master System as I haven't seen anyone else mention it here which kind of helps it's argument.

Bear in mind at the time it came out the NES was ridiculously dominant and Nintendo had almost full control of the market. Sega stepped in with a more powerful console and far less developers but still churned out great games for it that get very little mention nowadays. Titles like Asterix, Asterix & the Secret Mission, Master of Darkness, Golden Ax Warrior, Lucky Dime Caper, Psycho Fox, the Wonder Boy games, original Sonic titles and plenty of decent arcade ports for the time. Their phaser gun was better than the Zapper but got far less coverage and Sega even went experimental with 3d-like games (admittedly these sucked but fair play for the effort).

So yeah the Master System would be my pick.

For the US and Japan, certainly. For Pal regions and especially Brazil, not so much, where it was very competitive with the NES.

Xbox 360 is up there for me too.

One of the best systems ever in my estimation, with a massive library of awesome games and the better version of most 7th gen multiplats.

There seems to be a common myth that "from 2010 they only focused on Kinect" which just isn't true as in those latter years it still got a bunch of quality console exclusives like Gears 3/Judgement, Halo Reach/4, Splinter Cell Conviction, Alan Wake, and Witcher 2.

For my money, it actually has a better lineup of games than the PS3.

It's showing its age now but, for me, the 360 was the best console of all time.

This is going to sound weird but it's the Wii.....
Yes I know it sold bucket loads and transcended the mainstream but many people to this day just played Wii Sports for a bit and put it away. The console was waaaay better than that and had tons of great titles. I'm talking games like
Sin and Punishment Star Successor
Goldeneye 007 (remake)
Resident Evil Umbrella Chronicles
Super Mario Galaxy 1&2
Scarface
Mad World
House of the Dead Overkill
Guitar Hero 3
Punch Out
Silent Hill Shattered Memories
Metroid Prime 3 (and Other M)
Smash Bros
Zelda Skyward Sword
Mario Kart
Dead Space Extraction

And what about the Wii Ware titles?
Bit Trip Beat
Lost Winds 1&2
Contra Rebirth
Castlevania The Adventure
Fast Racing League

And what about that absolutely legit virtual console? Switch owners are still waiting for something of that calibre today and even the WiiU virtual console was inferior to the Wii's....

It's easily one of my favourite systems.

I was going through this thread and agreeing with just about every post, and then I got to this one.  I agree so much with this.  The Colecovision was the first console I grew up with.  People today tend to overlook it or downplay the impact it had at the time of its release because the North American Video Game Crash happened so soon after.  The Crash was another thing that I have seen people recently downplay as if it was an event that became overexaggerated over time.  But, it was very real for me growing up in the 80's.  I remember my father driving me to Toys R Us in the mid-80's asking for release dates on Coleco games which would never see the light of day. 

The Colecovision also played a key role in the development of the Famicom/NES.  Nintendo executives have stated that Coleco set the bar for graphical quality of home video gaming.  The two companies had several meetings which resulted in Coleco securing the rights to program and distribute the home versions of Donkey Kong and Donkey Kong Jr.

I'm not sure though what Pac-Man you are remembering though?  Atari had the exclusive home console rights to Pac-Man.  They did release an Intellivision version under their Atarisoft label that was much better than the 2600 version.  Atarisoft also created a prototype of Pac-Man for the Colecovision, but it was never released.  It was probably being worked on too close to the Crash.  Although homebrew versions do exist on cartridge format now.

In addition to the games mentioned on your list, other personal favorites of mine were:

Mr. Do
Bump n Jump
Donkey Kong Jr. 
Gateway to Apshai
Venture
Root Beer Tapper
Lady Bug
Mouse Trap
Carnival
Space Fury
Cosmic Avenger