Let's start with Rock Theatre.
https://www.discogs.com/de/mas…6234-Genesis-Rock-Theatre
This was released as early as in 1975 on vinyl, so naturally it covers only songs from the Gabriel era. Later it came out on CD too, the track selection remained unchanged. I had to get it on CD just for the sake of collecting.
I do enjoy listening to this one but admittedly it is quite odd: Its cover shows a photo from the Lamb shows (Peter as Slipperman), yet it does not include a single song off The Lamb. Instead it starts with I Know What Like - the only song off Selling England - concludes with Harold The Barrel and Harlequin, inserts Watcher of the Skies Single Version (!), and ends side A with Fountain of Salmacis. Side B entirely belongs to Supper's Ready. That's it. Judging by a number of comments, several people were tricked into believing this to be a live album, which would been pretty cool regarding the only official live album at that time was 'Genesis Live'. 'Rock Theatre' seems to pick particularly those songs that were missing on 'Genesis Live'. Except for WOTS which oddly appears in its rare single version... No matter what the selection seems somewhat random.
By any means, this remains the only ever compilation to include WOTS single version, also Harold The Barrel, Harlequin and Fountain are all quite rare choices you will hardly ever find on any Genesis compilation.
The Story of Genesis.
https://www.discogs.com/de/mas…esis-The-Story-Of-Genesis
This is the only one in the list I do not own, I included it because it looks to me as one of the best compilations listed on discogs.
Released in 1978, it covers all the albums from Trespass to And Then There Were Three. However, it was released exclusively in Japan and only on vinyl.
It goes chronologically through all the 70's albums and picks one track minimum, three tracks maximum off each album. Interestingly, it includes some rare choices: Dance On A Volcano, Eleventh Earl, and Burning Rope are all rarely found on other compilations.
Turn It On Again - Best of '81 - '83.
https://www.discogs.com/de/mas…It-On-Again-Best-Of-81-83
This was put out by Vertigo who owned the rights for Abacab, Three Sides Live and Genesis (Shapes). So these are the only albums that songs could be picked of. We get a number of Shapes songs: Mama, Home By The Sea (fading out before seguing into Second Home!), Illegal Alien, and oddly, Taking It All Too Hard; also Paperlate plus No Reply At All and Man On The Corner. Nice selection from that era so far but it really gets interesting when we get to the live tracks that follow: Misunderstanding, Follow You Follow Me, and Abacab are all live versions off Three Sides Live; the CD ends with two live versions that were only released on B-sides: the Turn It On Again Medley, and - the jewel on this one - a 1983 live version of Firth of Fifth.
Some people seem to have purchased this only for that Firth version. I like this compilation, it has its own oddness though with this selection. The live tracks make it much more interesting than other compilations. Also, this one is rare for including Taking It All Too Hard, also for fading out Home By The Sea, and even for juxtaposing Paperlate to No Reply At All. It's up to you what you make of this... Even more, this one is rare particularly for excluding I Know What I Like. IKWIL is the one song that appears on pretty much every compilation.
Turn It On Again (The Hits).
https://www.discogs.com/de/mas…Turn-It-On-Again-The-Hits
Released in 1999, this was the first ever compilation that could cover the band's entire career. Its concept is simple: hit singles only. With that, it relies heavily on the pop period of the band. It does include I Know What I Like though, plus Congo, plus Carpet Crawlers 1999. Overall it is a nice listen, with no surprises though. Notably, it does not include Tell Me Why.
Platinum Collection.
https://www.discogs.com/de/mas…nesis-Platinum-Collection
The first ever official compilation that covers the whole career of the band. 3 CDs including 40 tracks, it still appears to hold the record for most tracks on any Genesis compilation. It goes backwards-chronologically, picking between one and five songs off every album (except FGTR). Paperlate is the only non-album track; Calling All Stations is the only track clearly placed out of chronological order. Some rare picks on this one are: Behind The Lines, Undertow, In That Quiet Earth, Los Endos.
Turn It On Again (The Hits) - The Tour Edition.
https://www.discogs.com/de/rel…The-Hits-The-Tour-Edition
This seems to be generally regarded as a "version" of the 1999 Hits compilation, I always saw this as a compilation in its own right though.
Just like the 1999 compilation, this one too starts with Turn It On Again and closes its CD1 with Carpet Crawlers 1999 (also being the only other compilation to include CC1999 at all); just like the Platinum Collection it goes backwards-chronologically (with a few liberties) through the entire career. Rather than hits it focuses on single releases. Notably, this one does include Tell Me Why, also it includes Pigeons and Inside And Out - but omits Match Of The Day -, also Happy The Man and The Knife part 1. With five non-album tracks it has the highest number of non-album tracks on any compilation, also the highest number of Abacab album tracks (four). What's more, I'm pretty sure Afterglow wasn't a single release. Finally, just like on the Platinum Collection, the one CAS song (Congo) is placed completely out of chronology.
14 From Our Past.
https://www.discogs.com/de/rel…-Genesis-14-From-Our-Past
Since this has only been available in American Starbucks stores I could not get hold of it yet. Imports are quite expensive, otherwise I would have got it just for the sake of collecting.
Quite a simple compilation: 1 CD and it picks 1 song off each album (FGTR excepted) in forwards-chronological order.
Notably, it picks Happy The Man in place for Nursery Cryme, making Nursery Cryme effectively the only album left out; also it picks Squonk over Ripples or A Trick Of The Tail, The Lamb Lies Down On Broadway over Carpet Crawlers, and it includes Watcher Of The Skies which is a rare pick on most compilations.
R-Kive.
https://www.discogs.com/de/master/762988-Genesis-R-Kive
This one confused the hell out of fans both for its name and for its cover art.
As a Genesis compilation, this one is unique for including three solo tracks for each of the five core members, making up 15 non-Genesis songs. That aside, it covers 3 CDs and goes strictly chronologically (forwards) through the entire career, picking one to three songs off every album - FGTR left out as usual. This means its opening songs (The Knife, The Musical Box, Supper's Ready, The Cinema Show) alone make the first hour of listening. Compared to the Platinum Collection it has few surprises; it is notably though that it includes Back in NYC and the full album version of Tonight Tonight Tonight.
The Last Domino?
https://www.discogs.com/de/mas…9-Genesis-The-Last-Domino
Out of all the official career-spanning compilations this has to be the messiest of them all. It tries to replicate the live set list of the Last Domino tour by giving the full album versions of what was parts of medleys or at least live versions that differ a lot to the studio versions. The result is the most uneven track selection you could think of, even though the songs are great. It picks up to six (!) songs off each album, however it ignores anything pre-Selling England as well as A Trick Of The Tail. It favours on Selling England as well as Invisible Touch and it includes some very rare picks: Fading Lights, Domino, Dancing With The Moonlit Knight - all as full album versions - and Duke's End which ironically is the opener. Also, for a non-chronological compilation, it rows up to four tracks from one album: Domino, Throwing It All Away, Tonight Tonight Tonight (album version) plus Invisible Touch appear in this order while the four Selling England tracks are scattered all over the place.
It includes three songs that did not make it to the live set list: Jesus He Knows Me, In Too Deep and Abacab (single version!). Abacab is the only single version opposed to an entire collection of albums versions, adding just another oddity to this compilation. Other possible songs that didn't make it to the tour set list were not included: Blood On The Rooftops, Supper's Ready (for Apocalypse 9/8) should have been included. On top, Behind The Lines should technically have been included for Duke's Intro. Whatever... The Last Domino remains one of the weirdest compilations, official or unofficial.