There are so many great “best-of’s” that it’s hard to even know where to start. But I’ll go with The Best of Chuck Berry.
It was originally a single album, so you’re in the clear! 
That’s an interesting case, since a lot of those songs were issued on LP (in the UK) but not here. And even if it is kind of a catch-up package rather than a true anthology, I’d count at least four of its songs as “musts.”
Honestly, I’m not even that big a Beatles fan, but I don’t think any 45-minute anthology of their music could do them justice. You could probably do a good one for every year 1963-1970 they worked together.
“Legend” is a wonderful compilation, but there had been backlash from the beginnning from people complaining that almost none of Marley’s political songs landed on the album, with the exception of “Redemption Song”, and as such misrepresented his songwriting and larger impact. The label (Island) made up for it in 1986 by releasing “Rebel Music”, an equally strong companion piece with some of his deepest political anthems.
I thought the issue was that the songs were issued only on singles in the UK. British labels maintained an attitude that people didn’t like paying for the same song twice, so some singles weren’t on the LPs released at around the same time.
The album wasn’t released at all in the UK, and the songs didn’t make it onto an official Beatles UK album release until the Red and Blue albums in 1973. Except “Rain,” which was left off for mysterious (to me) reasons.
You’re probably right. I thought they were mostly songs from British LPs that were left off the American versions so Capitol could issue “new” albums with the leftovers, as happened earlier in their career with Yesterday and Today.
I nominate the Rolling Stones’ Made in the Shade, a 1975 release made up mostly of songs from Sticky Fingers and Exile on Main Street:
Brown Sugar
Tumbling Dice
Happy
Dance Little Sister
Wild Horses
Angie
Bitch
It’s Only Rock & Roll
Heartbreaker
Rip This Joint
It’s both great and completely inessential, since all the songs are awesome but you should already have all the original albums anyway.
As an album closer? Interesting choice, considering it’s such a perfect opening for Exile.
Don’t want to be the smart aleck, but the opener of Exile is “Rocks Off”. But it’s a two punch attack, second is “Rip This Joint”. I’m sure you knew this.
D’oh! I was getting the titles mixed up. That said, how could this anthology exclude “Rocks Off”?
Even more egregious, it omits “Time Waits For No One.”
This thread is heavy with nostalgia for me. My wife and I met as teenagers and I fondly recall driving around in her crappy yellow ford fiesta (I couldn’t afford a car) and listening to many of the albums mentioned here.
Certainly “Queens Greatest hits” “Legend” and “Standing on a Beach” were on constant replay. As was “live under a blood red sky” which may count and “Snap” by The Jam which a was a double album and so doesn’t count.
Best of the Doors* was the only Doors LP I owned as a child/teen, and it’s pretty great.
(True, their first album is an amazing debut as well).
*The 1973 single album one:
I always think of the Doors as one of the few 60s acts who couldn’t be represented by their singles, only by their album cuts. Not that the cuts on this compilation aren’t all good ones.
It’s a strange Doors respective that doesn’t include Break On Through.
Harpo and Jaycat, good points.
Here’s a much better example — the album I wore out when I was six years old, and is still as good today: