I reckon my favourite typing of all time would probably be the Flying type. There isn't really much of a specific reason, other than the fact that a lot of my favourite Pokemon are Flying types (Pidgey of course, as well as most of all the other starter birds, Lugia, the legendary birds, etc... Pretty much all birds haha), and the fact that there's always a spot in my party reserved for one. They're usually not all that strong, but they can still be a good addition. I mean look at Bird Jesus in the Twitch Plays Pokemon stream!
Fire and Water types are also pretty high up there, simply because of how strong and useful those typings end up being. Water types are pretty much always a necessity, since I don't think there's been a single game so far in which Surf hasn't been required. But other than that, it's also brought forth a lot of really beautiful designs. I mean Water and Ice types are probably some of the most elegant Pokemon so far, and I feel like there's always been a huge emphasis on how pretty the designs are when it comes to those two specific typings. And Water types are generally also really strong, being super effective against a bunch of types, while not having that many weaknesses.
Fire type Pokemon are mainly because of the emphasis of strength there is with the Pokemon, and it's generally just a pretty popular typing. I reckon part of it has to do with how a lot of them have relatively cool designs, and it's usually the Fire type starter of the various generations that's the most popular haha.