Probably what would happen is we'd start mass exterminating those species of pokemon that were dangerous to us and had been known to cause the deaths of humans. All we'd be left with would be cute pokemon and baby pokemon that would never evolve because it would be illegal to participate in pokemon battles since some group like PETA would say it's immoral to force your pokemon to battle (even if the pokemon themselves want to).
And even then, they'd only be very watered down versions of the babies, like maybe an Igglybuff that could tickle you or a cute little Eevee dog to have around the house as a pet that could maybe wag its tail in some remnant of what tail whip could once do...
There would probably be some secret organizations that had gone underground with a few of the pokemon that were not exterminated originally, so they'd be some of the few (maybe only) of their breed, andi f they were ever caught, they'd be arrested for keeping a weapon of terror around, and the human would be arrested on attempted terrorism charges and their pokemon would be put to death.
....If, on the other hand, we assume that most pokemon moves don't hurt all that badly and are more flashy than anything, I STILL think there would be extreme regulations on how to use them, since animal rights' activists groups would insist that we not battle with them, and they certainly wouldn't let us catch hundreds of them and keep them in poke balls on charges of animal cruelty. It's also unlikely that all but the most skilled of trainers would be able to have anything much more powerful than the cute little pokemon. The more powerful pokemon would mostly either be wild, in reservations/zoos, or owned by handlers specially trained to take care of powerful pokemon.
But most ordinary people would just own things that resemble our pets of today, like glameow and miltank and sentret and whatnot. We'd also probably just keep them as pets instead of letting them battle, since again that would probably be illegal to just do at home with no official referee, since they wouldn't want to deal with lawsuits of (my battling partner cheated and hurt my pokemon beyond what we had agreed on -- I demand that he pay my pokemon's medical bills and both of our emotional trauma from the event). So maybe if pokemon really demonstrated what they wanted to do was battle, they'd be allowed to in very specific places with trained pokemon medical professionnel and referees nearby, but it's unlikely.
So, yeah lol. Anytime I see an "I wish pokemon were real" or "what would it be like if pokemon were real" thread, I just think of how it wouldn't be anywhere near as exciting as we think it would, assuming we applied all the other properties of the real world.
...Ha, sorry. I was bored :P.