Be warned: #1 and #2 (last two entries) on this list contain spoilers for the end game so be careful.
Is the Moe-Eye a terribly useful capture? No. Is he absolutely needed or integral for anything outside of a handful of incredibly specific Power Moons? No, he is not. What he is though, is one of the most random and hilarious captures in all of Super Mario Odyssey. The Moe-Eye first appears in the Sand Kingdom but will pop up from time to time in other worlds. His ability? Putting on sunglasses. Doing so will allow Mario to see hidden paths at the expense of movement speed.
The Moe-Eye is not an incredibly convenient power, but just look at him. It’s a Moai Statue with a Mario mustache that hobbles around on tiny blocky feet with a pair of shades. While his lack of inherent usefulness keeps him from being anywhere high on the list, the quirkiness of its design serves as enough for it to make it onto the list.