Really it began with earlier editions of Basic D&D which it was a revision of. I'm not sure I would single it out any more then I would seperate 3.0 and 3.5.It's not quite the longest-running edition, but it's very close.
BECMI began with Frank Mentzer's Basic Set (the "B" in "BECMI"), which, presuming I have my dates correct, came out on May 1st, 1983. After this, the absolute latest I can find a BECMI-compatible product coming out from TSR is Troy Denning's The Classic Dungeons & Dragons Game: Epic Adventures with Wizards, Dragons, and Magic!, which came out on either May 2nd or May 4th, 1994 (I've seen conflicting listings). So BECMI lasted almost exactly eleven years.
(If you don't count that introductory boxed set as the ending point, then the last BECMI product would be the Poor Wizard's Almanac II, published on December 1st, 1993.)
By contrast, the AD&D 2E Player's Handbook came out in February of 1989, with the Dungeon Master's Guide following in May of the same year and the MC1 Monstrous Compendium Volume One following in June (I can't find exact release dates). Since the last AD&D 2E product was Die Vecna Die! (June, 2000), that means that if you start counting from when the PHB was released, AD&D 2E just barely edges out BECMI by a few months.
Please note my use of affiliate links in this post.
So far, no DM I'm playing with has let me walk in an change the rules at their table.I mostly want to take the pieces I like from the editions I've played and slap them onto 5e.
I know! It's just so frustrating that The High Council of Gaming prevents us from doing that.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.