As others posted, this is a typical age for this behavior. Unfortunately. My son was the mellowest toddler (and usually on the receiving end of hits by older friends) until about 3 days before his 3rd bday, then turned into a 'terrorist', we were shocked (like others said) and not expecting it at all. Since he was a premie and regularly seen by a developmentalist, serious issues were ruled out and it was chalked up to the age and normal behavior. It was also around the same time that he was phasing out his one nap and as much as I tried to keep that consistent, it wasn't happening.
I would repeat to him, simply and matter-of-factly, "we don't hit you, so don't hit us" or "____ doesn't hit you, so don't hit ____" and redirect him. It usually took just one direction at that instant, but it went on for a while. I can't really remember when it stopped, he's 4-1/2 now, but I can't remember the last time he did it. Now it's more about hitting in defense, like at school, he spilled his milk, for whatever reason a girl kicked him hard, he punched her back. They both got warnings and separated. The teacher said he was very receptive, apologized immediately and understood the punishment. Then us moms had them hug it out after class. So there was that good part about it, haha. Now it's a challenge of how to teach him to stand up for himself, but not harm others, ask for help, but not tattle. It's always something!