Psychic-types have a lot of Pokémon with various kinds of appeal while maintaining some smartness associated with the type.
A lot of Legendary Pokémon I like also happen to be Psychic-types.
It helps that they're the absolute best type in Kanto in Gen I. Even after the subsequent nerf in Gen II, some could still learn a variety of special moves like the Elemental Punches. After the physical/special split in Gen IV, many did take quite a hit, but as soon as we got the Fairy-type and Mega Evolutions in Gen VI, many have also bounced back into the competitive environment.
My favourite Psychic Pokémon are Mewtwo, Alakazam, Espeon, Metagross, Lunala, Lugia, Starmie, Hoopa, Mr. Rime and Gardevoir.