Yokai-watch is Japanese and had an influence on Pokémon(heavy influence on Sun and Moon). In terms of scope and popularity, it's hard to say what the American equivalent would be but I'd argue four distinct franchises, maybe five could be considered as rivals but not quite fitting into the category that Pokémon resides.
The first one is Star Wars. This franchise has been around forever and has numerous titles, movies and other stuff to its credit(including two animated series that were exceptionally well done). The games occupy multiple genres, the most notable of which is FPS and Flight Sim(although it did touch RTS and MMORPG).
Second one is Star Trek. Fans are called Trekkies and like with Star Wars has numerous movies, games and other merchandise. Alas it doesn't have any animated series to its credit(AFAIK) so it doesn't quite fit the mold if we are being picky. However, it's longevity is incredible and that's why it's on this list.
Third is Transformers. This franchise back in the 80's was huge... Toys that were made back then are collectors items and with the new generation of movies that keeps Michael Bay employed, the popularity has been revived. Tack on numerous animated series and this franchise rightly deserves to be on this list.
Fourth would go to Teenage Mutant Ninja Turtles. This franchise has been around for decades and has undergone numerous incarnations. Several video game titles to its credit, along with several movies, this franchise deserves to be there.
Fifth would go to Comics, specifically DC/Marvel. If you want animated series, these two platforms dominate children programming. Be it back in the 80's, 90's or now, there are several series with characters from those franchises. The recent movies have reignited interest as I see it so of this list, I'd pick this one.