Musical:
Green Day's original gig becomes their only outing.
Britpop, rather than the Second Wave of Blue-Eyed Soul (Adelle et al), becomes the Third British Invasion.
Instrumentless Boy Bands (Like New Kids on the Block and Boys 2 Men) rather than Grunge, replace Hair Metal.
90s Style Young Country had broken out ten years earlier, and had been the country music sound to eclipse Outlaw Country rather than Neo-Countrypolitan. Garth Brooks was okay, but he spawned a bunch of terrible imitators.
The Who concert crush in Cincinnati destroys their career.
The Who breaks up after the explosion on The Ed Sullivan Show causes one or more major casualties among the band.
Michael Jackson's hair accident kills him.
Computer and Video-Game:
Hewlett-Packard buys what would one day be the Apple I from Steve Wozniak, then sits on it.
IBM forcibly buys out Microsoft, then goes on a production ramp-up, while the Reagan Administration fires all the Anti-Trust prosecutors and drops all charges.
Apple goes for Project Star Trek- in 1987.
The Stanford, Berkley, IBM, and/or ARM RISC projects never happen.
No one bails out Hi-Toro Labs.
Atari takes the Nintendo deal, then sits on it, in a way enforceable by any court outside of Japan.
NEC never buys the design of the PC Engine off of Hudson, and Hudson goes bankrupt from Nintendo reneging on the original deal.
Coleco doesn't have Cabbage Patch Kids to bail them out.
Microsoft files a lawsuit against Fujitsu over the F.M. Towns, and wins, alienating game publishers, but without a viable alternative because Apple is overpriced and all business (Except for Bungie), the Amiga and Atari still go down the tubes, and Acorn still never gets its $#!+ together with the Archimedes/RISC PC.