Back when Lemmings defined the genre known around these parts as the "Interactive Rodent Simulation", British games magazines half-jokingly termed it a "Save 'em Up", to match the then-common names of popular genres such as "Beat 'em Up" and "Shoot 'em Up".
As we all know, a Save 'em Up is not a game where rescuing someone or something is merely a later objective or part of the plot (as is the case with rescuing Princess Peach in Super Mario Bros., for example), but a game where the entire point of the gameplay hinges on this mechanic, as it does in Lemmings - otherwise, quite a lot of unrelated, non-Save 'em Up games could be counted as Save 'em Ups, and then things would get confusing.
It's often been said that Lemmings was the first game where the main gameplay objective is to save helpless creatures, but, whilst Lemmings is (as far as I know) the first game to play as it does, it was not the first Save 'em Up. There are actually at least six earlier games of this sort, and it seems to me that, whilst lists of "Lemmings clones" exist out there that include both commercial releases and fan-made ones, commercial releases in the Save 'em Up genre as a whole could stand to be better-documented. The following is the beginning of an effort to do so (in chronological order) - please contribute or suggest games that need listing if you find the idea interesting!
The first Save 'em Up that I'm aware of is the Nintendo Game & Watch game,
Fire, released in 1980. In this game, you move two firemen who are holding a trampoline, in order to rescue people who are jumping from the windows of a burning building. It has been remade a few times, with both classic and modernised forms, in various installments of the Game & Watch Gallery series for the Game Boy, Game Boy Colour, and Game Boy Advance.
The second game is
Cosmic Ark, which was made by Imagic for the Atari 2600 in 1982. To the best of my knowledge, this is the first example of a Save 'em Up on a home machine (and it's also the first known sequel to a home video game, too!). Cosmic Ark's premise involves piloting a spaceship to distant planets in a dying solar system, in order to rescue the creatures that inhabit them so as to prevent their extinction. This is the first Save 'em Up that involves saving animals from a terrible fate.
The third entry here is the coincidentally-titled
Lemming Syndrome, by Dynabyte, released in 1983 for the BBC Microcomputer (a series of computers which were commonplace in British schools in the 1980s and 1990s, and which occupy more-or-less the same cultural space as the Apple II does in North America). It's really just a clone of Fire that's set on a broken bridge, but it lacks the differing heights for the people doing the jumping.
The fourth Save 'em Up title is
Flicky, an arcade game released by Sega in 1984. In it, you guide a bluebird named Flicky around platform-filled levels in order to gather up chicks (known collectively as Chirps), who will follow him around until they're either hit and broken away from him by an enemy (at which point Flicky needs to grab them again), or until he takes them to each level's exit.
The fifth such game that I know of is the Commodore 64 version of the Dizzy series spin-off game,
Kwik Snax, released by Codemasters in 1990. There is a ZX Spectrum and Amstrad CPC game by this name as well, but it is actually completely different and, crucially, it is not a Save 'em Up. Kwik Snax for the C64 basically puts the game-mechanics of Flicky into a top-down, Pac-Man style maze, in which you have to guide Dizzy around so that he can gather up small, rodent-like creatures known as Fluffles. This seems to be the first Save 'em Up to be centred around rescuing creatures of the rodent persuasion.
The sixth pre-Lemmings Save 'em Up that I know of is a special case. It is
Save Mary! for the Atari 2600, and it was completed and due for release by Atari in 1990 (after apparently having been worked on since 1988), but ultimately never made it to the market at that time - it was not actually officially released until it was included in the game selection on the
Atari Flashback 2 console in 2004. In Save Mary!, you must drop girders and blocks into a quickly-flooding valley, so that Mary, who is trapped at the bottom, can climb up to safety before she drowns.
I don't know of any other pre-Lemmings Save 'em Ups, so I guess up next is Lemmings, and everything that came after it (including its own sequels).
That said, I'd like to wait for more input first, just in case any other early commercially-released Save 'em Ups that I don't yet know about exist.
Incidentally, if I've put this in the wrong section, please could a moderator move it? I honestly wasn't sure if it should go in Lemmings Discussion (since it's about documenting the genre that Lemmings undeniably defined), or in the Video Games section in Off Topic (because it deals with a lot of other games as well).