What are your favorite supergroups?

One is The Power Station.

Robert Palmer

John Taylor (Duran Duran)

Andy Taylor (Duran Duran)

Tony Thompson (Chic)

That's another fuzzy definition with respect to the "fame" that makes the "super" part. For example, Cream was considered a supergroup in the UK because all three musicians had some measure of fame there, but in the US only Eric Clapton had any name recognition, and just barely because of his short stint in the Yardbirds.

Otherwise, I can't say that I ever warmed to the idea, and after a while it seemed like a marketing gimmick to revive flagging careers. Probably it was the synthetic prog-pop of Asia that really disabused me of the idea. And I like John Wetton as a singer and bassist.

Maybe Derek and the Dominos? But like Blind Faith, that seemed to be a one-off idea and not viable in the long run.

Actually, I can think of one that I've seen within the last 10 years: The Five Peace Band with Chick Corea, John McLaughlin, Kenny Garrett, Christian McBride, and Vinnie Colaiuta. However, they're at best jazz-rock and may not fit fully in a Rock discussion board.

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"The past is never dead. It isn't even past." -- William Faulkner

You are obviously knowledgeable about music.

I almost mentioned Cream as one of my favorite supergroups. But I am American and most Americans don't think of them as a supergroup. And a lot of casual fans think of them as "Clapton's old band".

By bro lives for progressive rock and abhors the band Asia. They had one huge selling album then hung around with different lineups off and on for years. I think a lot of supergroups are just projects and maybe recording only one album might be appropriate. You probably know that Trevor Rabin auditioned and was considered for Asia. Rabin said that his involvement with the band never went anywhere because "there was no chemistry".

I almost mentioned Cream as one of my favorite supergroups. But I am American and most Americans don't think of them as a supergroup. And a lot of casual fans think of them as "Clapton's old band".
To answer your original question directly, I too would pick Cream as my favorite supergroup. (They would also qualify for your question about power trios.)

I think a lot of supergroups are just projects and maybe recording only one album might be appropriate.
That's a good assessment. Certainly Clapton's group after Cream, Blind Faith, had that feel to it--and the band's name alone seemed to indicate their lack of confidence in such a project. They only lasted for one official album, anyway, and much of that sounded like Steve Winwood's previous band Traffic.

You probably know that Trevor Rabin auditioned and was considered for Asia. Rabin said that his involvement with the band never went anywhere because "there was no chemistry".
Not surprising, as the whole idea sounds like an all-star team--they may wow the crowd for one game, but over the long run they won't be feasible. Rabin did go onto Yes, and although purists don't usually like the band's early-1980s material, I thought it was appealing prog-pop--certainly no worse than Asia.

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"The past is never dead. It isn't even past." -- William Faulkner

Critics and fans (of the original groups) did not seem to like them, but I liked the music of Audioslave and Velvet Revolver.

Audioslave for me was an opportunity for the RATM guilty parties to divert their music from RATM and utilizing the vocal power of Chris Cornell, which de la Rocha did not have. And also to lay back from the norm anger of RATM.

Velvet Revolver were beginning to gel and IMO was one of the last 2000 era groups playing 80s hard rock music. I was disappointed when they broke up and that the 2nd album was their last. We now know it is their last with GnR members getting back and reforming the W Axl Rose and Backup Band group, and with Scott biting the bullet.

Do you like Temple of the Dog? I just heard they are touring. Please click on
http://consequenceofsound.net/2016/07/temple-of-the-dog-announce-first-ever-tour-dates-for-25th-anniversary/

I like Temple of the Dog. Well Hunger Strike anyway.

Ditto.