The KLF discography is extremely huge, considering they only had few major hits. Their backcatalogue consists of plenty of limited editions, remixes and unreleased records in addition to normal singles and albums. I'm here trying to present the most essential selection, the records that are most important for everyone who are interested in this group, but are not hardcore fans.

Selected discography AKA Essential The KLF

The Justified Ancients of Mu Mu - All You Need Is Love Single 1987
The JAMS - 1987 (What The Fuck Is Going On?) LP 1987 * had lots of illegal samples and had to be withdrawn from the shops

The JAMS - 1987 (The JAMS 45 edits) EP 1987 * free of illegal samples
The JAMS - Down Town Single 1987
The JAMS - Who Killed The JAMS? LP 1988
The KLF - Burn The Beat Single 1988
Disco 2000 - One Love Nation Single 1988
The Timelords - Doctorin' The Tardis Single 1988 * 18 singles released
The KLF - What Time is Love? (Pure Trance Original) Single 1988 * 5 singles released, one limited to 3 copies only
The JAMS - History of The JAMS AKA The Timelords (Compilation) LP 1988
The JAMS - Circa 1987: Shag Times (Compilation) 2xLP, CD 1989
The KLF - 3 A.M. Eternal (Pure Trance Original) Single 1989
The KLF - Kylie Said To Jason Single 1989 * 7 singles and promotional video
The KLF/Various Artists - The "What Time is Love" -story LP 1989 * covers of "What Time is Love?" by other bands
The KLF - Chill Out LP 1990 * reissued on CD in 1991, 1993
The KLF - Last Train To Trancentral (Pure Trance Original) Single 1990
Space - Space LP 1990
The KLF - What Time is Love? (Live at Trancentral) Single 1990/1991 * 40 singles released, including 2 VHS videos.
The KLF - Waiting (Video) 1990
The JAMS - It's Grim Up North Single 1990
The KLF - 3 A.M. Eternal (Live At The S.S.L) Single 1991 * 26 singles released, including one VHS video
The KLF - The White Room LP 1991
The KLF - Last Train To Trancentral (Live From the Lost Continent) Single 1991 * 25 singles released, including one VHS video
The KLF - Stadium House (The Trilogy) Video EP 1991
The KLF - America: What Time is Love? Single 1991 * 20 singles released
The JAMS - It's Grim Up North Single 1991 * re-release
The KLF - Justified And Ancient (Stand by The JAMS) Single 1991 * quest vocals on one track by Tammy Wynette, 25 releases including 2 VHS videos
The KLF - Rites of MU Video 1992
The KLF with Extreme Noise Terror - 3 A.M. Eternal Single 1992 * LTD edition single only available through mail order. last official release.
The KLF - This is what the KLF is About I CD 1992 * 3 cd singles - What Time is Love, 3 A.M. Eternal, Last Train to Trancentral
The KLF - This is what The KLF is About II CD 1992 * 3 cd singles - Justified And Ancient, America: What Time Is Love, It's Grip Up North
Jeremy Deller Presents 2K - ***K the Millennium (Produced by the Artists forever known as THE JUSTIFIED AND ANCIENTS OF MU MU) Single 1997

Most of these releases were released on their own label, The KLF Communications.

Take note: When counting the amount of releases, the count includes remix ep's as well as licensed releases to other labels.
Also, I've listed official releases only, not promos or planned releases.

Discography sources: various online discographies, my record shelf