The last Pokemon game I played was Sapphire on the GBA. I recently decided to get back into it, starting with the game after Sapphire GBA, Pokemon Diamond. Coincidentally, I rewatched a lot of Always Sunny while playing and decided to pick some Pokemon from the 151 pokedex of Diamond that corresponded with the characters.

Mac-Geodude, Mac thinks he's tough, Geodude thinks the same. Also Geodude never works legs, just like Mac.

Dennis-Roserade, Dennis and Roserade seem very conceited about their looks, with no real basis.

Sweet Dee-Pelipper, obviously a large bird with a big mouth.

Frank-Abomasnow, short, those eyebrows are similar to Frank's, and Frank generally has an icy demeanor toward everything.

Charlie-Psyduck, most things confuse Charlie, most things confuse Psyduck.

 Always Sunny has quite a few supporting characters that appear throughout the show that add a little something extra, so I had to choose Pokemon for them as well.

Artemis-Honchkrow, both puffed up, think they look sexy and I'm fairly certain Artemis would wear a hat just like that if she hasn't already.
Rickety Cricket-Gastly, Cricket should most definitely be dead with all the things the gang and life have thrown his way, but he isn't. Bonus, since Cricket used to be a priest, but in episodes after becoming homeless, makes fun of religion, so perhaps he's being punished to roam the mortal world.
Ryan McPoyle-Croagunk, both appear to have their mouths constantly open and their statures are fairly similar. Croagunk can be found in the Great Marsh and the McPoyles probably originated in a swamp.
Liam McPoyle-Toxicroak, all of the same reasons for Ryan, except Liam is the McPoyle who is more in charge. Toxicroak's pointed head is also similar to Liam's hair.
Margaret McPoyle-Bidoof, both are more like set pieces than actual living things.
Waitress-Bronzor, this one was hard, the Waitress has no real personality traits other than her problems with alcohol. The Gang barely notices her and is annoyed by her, Charlie loves her/stalks her, and then she is subsequently annoyed by him. I chose Bronzor because if you tilt him horizontally, he becomes the perfect tray and trays are necessary for waitresses.