It's always tempting to get on a high horse when Hollywood changes an ending, and plenty of the YouTube posters do just that. Personally, I think the producers were completely right to alter the stage conclusion for a film, in a way that says something quite interesting about the two media.
A little bit of history here - Little Shop of Horrors was originally a 1960 horror/comedy, shot in two days by legendary schlockmeister and cheapskate Roger Corman to take advantage of some sets he had left over from another film. Scripted by Charles B. Griffith (who had used more or less the same plot for A Bucket of Blood the previous year), it's a Faust-variant, about a downtrodden florist's assistant, Seymour Krelbourn, who discovers fame and fortune thanks to an unusual plant in his basement, which after a time, starts to demand human blood.
Seymour becomes one of the cinema's few sympathetic mass murderers. Like David Warner in From Beyond the Grave or Claire Higgins in Hellraiser, he kills to keep another character alive - on one level, he's a symbol of everyone who's ever done a job they hate for the sake of a mortgage, a child, a spouse, or - given the film's Jewish milieu - a nagging momma.
When Howard Ashman and Alan Menken adapted the film as a stage musical in 1980 they played down the Jewishness, but raised the racial stakes in other areas, adding a girl group-style chorus (called Crystal, Chiffon and Ronette) and giving the plant musical and speech patterns ('No shit, Sherlock!') that make it clear that, in this case, green is the new black.
Located in a 1960 that had become a period setting, the musical shows an Eisenhower-era America that's just about to be blown apart, not just by carnivorous plants, but also by MLK, Malcolm X and Motown. The film version makes the connection explicit by having the plant voiced by Levi Stubbs, of the Four Tops.
On stage, the plant is unquestionably the star, whether played by a multiple-operator puppet or - as in a superb production I saw in Edinburgh in the late '90s - by the whole cast as a green-clad chorus, gradually adding members as new victims get eaten. When Seymour sacrifices Audrey (the heroine) to the plant, it's an epiphany, accompanied by apocalyptic Phil Collins-ish drums.
Frank Oz, director of the 1986 version, argued that the stage ending works because the audience knows that Audrey and Seymour are going to be back for the curtain call, which isn't the case on film. I think there's a more profound difference, to do with the way that we participate in the two media. As a theatre audience, we take on a collective identity, sharing time and space with the performers; in the cinema, we remain a group of individuals alone in the dark. (There are exceptions - when I saw The Cook, The Thief, His Wife and Her Lover, the audience emerged from the cinema like a group of people who'd been through a war together.)
In the cinema, we tend to favour the individual, even if he's a murderer, over the group; in the theatre, it's the other way round. In the film version, we want to see Seymour and Audrey survive and get together; on stage, it's the plants that we're (ahem) rooting for.