Fighting, poison, and flying.
I like fighting because many of them are clever takes on real life fighting styles and rely on mastering actual technique(though it helps they usually have super-level physical prowess as well) as opposed to just farting out fireballs or vomitting lasers. Plus they seem like they'd be really cool to see in action since their moves tend to have a lot of oopmh to them on impact. They're the DBZ fighters of pokemon, and that's awesome. My favorite fighting types are probably Megalopunny, Infernape, Mienshao, Scrafty, and (Mega)lucario,
Poison I grew to like admittedly because for the longest time it was quite an underappreciated type. Many of the pokemon weren't too cute, it stunk offensively(sometimes literally), there wasn't a lot of powerful poison moves, and it seemed cowardly compared to just blasting your opponent with fire or whatever. But I felt like defensively it was always solid enough and with a mix of patience and cleverness, you could end up doing some fine work with them. 4th gen is where I started to gain a bigger appreciation for poison due to toxicroak and drapion mainly, then gen 5 added scolipede(garbador too) and I figured that hey, I can finally make a poison monotype team with pokemon I all like. But gen 6 is what set poison from being a type I liked to one I loved, as it got some very nice buffs in the fairy factor as well as 3 megas, all of which are good(and one that's VERY good). Toxic spikes is also a really cool move and poison is the one type that's only gotten better and better as the game has evolved, something that can't be said for every type. My favorite poison types are Drapion, Scolipede, Gengar, Crobat,and Nidoking.
Flying has recently taken over steel as my 3rd favorite type. Now I always liked flying but found them a bit boring since fly was what I'd alwas end up using in the main games. But after playing a monotype flying run in reborn my love for the type grew and I've found myself loving the supportive potential of flying types with tailwind and defog plus roost allowing more defensive fliers to last quite a long time in battle. The diversity in flying types I feel is second to none and keeps flying monoruns from ever feeling too limited(though I suppose they do end up easier as a result). They also sport some very powerful pokemon, including some of the strongest ubers. On another note, Skies of Arcadia is one of my favorite games of all time and flying is a pokemon type that alludes perfectly to the game, so that's a plus too. My favorite flying types are Staraptor, Sigilyph, Gliscor, Togekiss, and Emolga.