Aside from ROM hacks and fan games, which there are by the truckload, and I personally think are the best option, there's a slew of nice alternatives to Pokémon that are worth checking out and are sure to scratch the itch. Off the top of my head there's Nexomon, Coromon, Automon, Monster Crown, as well as Siralim Ultimate and Monster Sanctuary. Add to those Cassette Beasts, Creature Keeper, and Totama, which are still in development, alongside a host of others that show promise. And of course there's also the other more official "clones" like Digimon, Monster Rancher, Monster Hunter Stories, and Ni no Kuni.
EDIT: Oh yeah, and there's also Eternal Eyes for PS1.
First thing's first: I returned to this topic because I wanted to add to the list I posted, but I'm sitting here slapping myself because, of all the games that I named, even after coming back to make an edit, I can't believe I didn't mention the Dragon Warriors/Quest Monsters series. That's unforgivable. Might as well add to that Yo-Kai Watch and Spectrobes.
But anyway, here's an addendum to my previous list...
Anode Heart, Phobies, and Moonstone Island for PC, as well as Robotrek, Metal Walker, Monkey Puncher, and DemiKids for SNES, GBC, and GBA, respectively. There's also the Fossil Fighters series for NDS/3DS and Dinosaur King for NDS, which really isn't as bad as some used to say back then. Another dinosaur-related "clone" would be GachaSta! Dino Device for GBA, which not only comes in the same flavors as the original Pokémon games, but as the name implies, it revolves around gachapon; it also has a sequel, but unfortunately none of the games have been translated yet. Another possible option would be the Medarot/Medabots series, and although it only has a few of the games localized in the West, fan translations have popped up over the years for a handful of them and are readily available. Next to those would be Network Adventure Bugsite for GBC, which involves a virtual world over the Internet accessible with VR equipment, where you play as a virtual entomologist, or a "Hacker", that catches "Bugs"—it stayed in Japan, but there's a fan translation project that has been casually updated throughout its inception. And of course, there's Robopon for both GBC and GBA, the former being of particular note given that some would declare it doesn't hide the fact it's a "shameless rip-off", albeit a good one, all things considered (there's also a game for N64, but it hasn't been translated, unfortunately).
And, speaking of rip-offs, Telefang is yet another alternative that notoriously began its life in the West as a Pokémon knockoff when its versions were passed off as bootlegs named "Pokémon Diamond" and "Pokémon Jade", with the actual games behind these being Keitai Denjuu Telefang Power and Speed, respectively. Similar to Robopon, there was also a set of games released for the GBA that once again got bootlegged as Pokémon games. As alluded to, this franchise never made it overseas, but there are fan translations available.
Lastly, in addition to all that, there's a game for NDS called Monster Racers that's like Pokémon, but as the name implies, it's all about competing in races instead of battling, sort of similar to Pokémon Dash. And I guess we could include Elebits: The Adventures of Kai and Zero for NDS and Lil' Monster for GBC, the former which doesn't quite follow the same formula, while the latter simplifies it, as one would infer by its name.
Honorable mentions: Barcode Taisen Bardigun, Monster Traveler, GB Harobots, Kaseki Sousei Reborn II: Monster Digger, and Space-Net Cosmo Blue and Cosmo Red for GBC; Zettai Onkan Otoda Master and Dragon Tamer: Sound Spirits for NDS; and lastly, Zool: Majuu Tsukai Densetsu for N64. These are some really neat-looking games that, as of this writing, have yet to be translated.
