The greatest Greatest Hits album ever?

Queen's three-disk one.

Metallica - S&M
not really a greatest hits album but I think it qualifies xD

The Best Of Pink Floyd: A Foot In The Door

I don't listen to Greatest Hits albums. I'm a hipster.

Frank Sinatra's Greatest Hits.

Queen 1,2,3, AC/DC and Bob Marley.

I don't listen to them. Or more accurately, none of my favorite bands have any. Although I think The Legendary Pink Dots has plenty of collection albums, so maybe I'll answer "any of those".

I'll add Sting, Foo Fighters and the Red Hot Chili Peppers greatest hits.

I don't listen to greatest hits albums. Most of my favorite songs by my favorite artists aren't hits anyway, and I like to experience albums the way they were intended, not in some meaningless selection made only to rip off the fans by putting one or two new songs in there. When that happens, I only keep the new songs and delete the rest of the greatest hits. Or when the new songs are released as singles, even better, I only keep the singles.

I have quite a specific taste in music and I tend to like listening to whole albums that have been composed such that they flow well as a single entity, not just as individual songs. So, this being pretty much the antithesis of the 'greatest hits' concept, I don't listen to such collections at all.

In Time: The Best of R.E.M. 1988–2003

Bon Jovi Cross Road, my dad has that disc in his collection and I remeber one afternoon when he put "Ill be there for you" on the cd player and the song just hypnotized me, I had to listen all the disc after that.
I have been a Bon Jovi fan ever since.

Don't listen to compliation albums much but love Meaty Beaty Big and Bouncy (The Who).

I'm gonna throw my hat in for Queen and Metallica S&M. Jimi Hendrix Greatest Hits is pretty good too.
The Beatles have been mentioned, but they have albums that are better than their greatest hits compilations, so, um, no.

I also want to point out that there's a difference between "greatest htis" and "best of", though I doubt anyone cares.

So hard to tell only one, I'll mention a few I recall as impressive song collections as 'best of' albums by some of my favourite artists:

The Very Best of The Beach Boys
The Best of The Doors
40 licks (by The Rolling Stones)
The Very Best of The Stone Roses
The Sound of The Smiths
Kiss This (by Sex Pistols)
Echoes: The Best of Pink Floyd
Greatest Hits (Bob Dylan)
My Generation: The Very Best of The Who
Standing on a Beach: The Singles (by The Cure)
Galore: The Singles 1987-1997 (by The Cure)
...

Lynyrd Skynyrd - Gold & Platinum

[:SITD:] - Bestie:Mensch. Pure masterpiece of electronic music.

Edit: Pink Floyd A foot in the door.

Experience Hendrix

Idk if greatest hits but Aerosmith "Big Ones"

Simon and Garfunkel's Greatest Hits from 1972. I usually don't listen to the greatest hits because I like almost all of their music and they don't have that many albums, so I just end up listening to it all.

I also really like Peter Gabriel's 2003 album "Hit", but they left out some good songs like In Your Eyes and Mercy Street.

REM's "Out Of Time" from 1991 isn't a greatest hits, but it feels like it to me because it was the first REM album I grew up from a really young age and I like all the songs.

The Best Of Van Morrison (1990)

Best of The Doors

honorable mentions:

Billy Joel Greatest Hits – Volume I & Volume II
O, Yeah! Ultimate Aerosmith Hits
Flashback: The Best of the J. Geils Band
Foreigner Complete Greatest Hits
Bob Seger Greatest Hits
Lest We Forget: The Best Of Marilyn Manson
Gun N' Roses Live Era '87–'93 (not technically greatest hits but qualifies to me)
AC/DC Live! (same as above)

Not so much a greatest hits, but the best album ever produced:
Iron Maiden: Powerslave.
but if we are doing runners up:
Mr WubbleStien was on track with The Best Of Van Morrison (1990)
Steve Earles' Copperhead Road
Aerosmiths Pump
The Offspings Smash
Alice Coopers Trash
The Waifs Greatest Hits So Far
The Violent Femmes Debacle
Greendays' Dookie
And Metallica's last good album, Black (self titled).
Edit
OMG... Almost forgot Tom Waits: Mule Variations - I humbly beg forgiveness!