Pokemon, Monster Farm: Enbanseki no Himitsu Recommendations
Both invlove a variety of bizarre creatures that do battle and are based on video games. Monster Rancher's quite a bit darker than Pokemon, but still primarily directed at children.
Both shows showcase Monsters, Friendship, Lovable side-kicks and Main characters wearing hats (and a not giving-up till i die personalities), though Monster Rancher has deaths while Pokemon does not.
Both shows from the same era that focus on young protagonists who capture and befriend monsters. In both our heroes form deep connections to their respective monsters and encourage them throughout battles and help them to grow stronger.