Out of all of the 'side-events' in the gaming series (Contests, Musicals etc.) the Pokeathlon is easily my favourite out of all of them. Mainly 'cause it requires skill on the part of the player in the moment, instead of simply hours and hours of berry feeding/scarf sashaying. Obviously that's still a part of the Pokeathlon, but I liked how it wasn't the be-all-and-end-all. The integration of the DS' touch pad was really well done and the whole thing is an example of a side-event done well.
As for favourites, I liked the Hurdle Dash, the Relay Run and the Block Smash. I managed to excel in those whenever I tried them out. The Speed contest in general was always my go-to one, as well, as my team had a lot of fast critters in it. (Helloooooo, Aerodactyl! :D)