N64... I know the sales were awful compared to PS1 but I still play it today and it still has value for couch co op in 2019.
4 players, rumble paks, analog sticks and progressive scan graphics with a 100mhz 64 bit processor and 8MB of RAM once expanded. It was a beast in the day.
Anyone still keen to play their PS1? Didn't think so!

For me, it's gotta be Xbox 360.

Massive amount of good to great games, the superior (console) version of most 7th gen multiplats, Gears + Halo, and one of the most comfortable controllers out there.

Still my #3 fav console of all time, with only SNES and Wii ahead of it, and both only slightly.

N64, with GameCube and Dreamcast as a distant 2nd and 3rd. N64 had some amazing 4 player mutiplayer titles while GC and DC just were underrated in general with some really solid single and multiplayer games. 

I don't really consider 360 much of a loser as it was nearly even with PS3 and was by far MS's most successful console. 

Perhaps "loser" is a bit harsh, it's just a catchier thread title pun. As I explained, I'm simply referring to consoles that didn't win their gen in sales.

1. PS3
2. SEGA Genesis
3. PSP

I don't really consider PS3 and Genesis as losers.
But going by OP definition my favorite is by far PS3 and Genesis have a lot of love from me as well.

In my other post in this thread, I said Xbox 360. While a loser, it was still what I'd consider a huge success.

My favorite inarguable loser is definitely the Dreamcast. I actually hated Sega and I was happy to see the Sega Saturn so soundly stomped by superior systems. Fast forward to early 2001 and no matter what I did, I couldn't get a PS2. Frustrated, I finally gave up and bought a Dreamcast. What a fool I'd been!

This thing blew away my every possible expectation. I was buying great game after great game. Graphics were light years ahead of what I'd experienced on N64 and PS1. The machine was full of exciting innovations, too. Maybe a week (that's how I remember it) or maybe a month after buying my Dreamcast and bragging about games like Shenmue to my PS2 owning friend, I watched sadly as Sega announced they were leaving the business but still supporting the Dreamcast for one year. Then the price dropped $100--a lot of money for me at that time.

In March 2001, I finally got my own PS2 with copies of The Bouncer and Zone of the Enders (with NBA Street, Red Faction, and Onimusha to follow). After a couple of weeks, I was right back to my Dreamcast. Say what you will about the PS2 but up until maybe November 2001, no PS2 owner alive was having as much fun with their console as I was with my Dreamcast.

I know the PS2 is considered one of the best console ever, it certainly sold the best.  But it was my least favorite PlayStation console.  I enjoyed the Gamecube quite a bit more than my PS2.  I also wished I would have gotten the Dreamcast, I thought about getting it so many times back than, especially when the price dropped.  I've never owned a Sega system, but I still kind of regret it.  I keep hoping we will get Skies of Arcadia brought back, as I missed out on that game on the Gamecube, but it looks terrific. 

I'm actually right there with you on the GameCube. I think Nintendo just didn't market it right. It was truly amazing. My favorite console of the gen.

Also, it's good to see you have an open mind. Something I had to learn the hard way. Most consoles are worth owning. We only hurt ourselves when we're afraid to at least try something new. And yeah, Skies of Arcadia was AWESOME.

The Gamecube. In addition to the NES, they're the only two generations I've been fine with only having Nintendo's console. Of course I wasn't going to miss out on playing games like Halo and God of War completely, but there wasn't enough there for me to feel like I had to own another console that generation.