Here's what I'd imagine, on which characters in the main cast (as well as a few secondary characters; not including alt. universe versions of characters) had their own pokemon companion.

Main cast:
= Homestar Runner -> Lucario
= Pom Pom -> Hitmonlee
= Marzipan -> Ribombee
= Strong Bad -> Zoroark (Hisuian) (I imagine he would also assist the elderly Senor Cardgage, when not helping the MAIN universe version of Strong Bad!)
= Strong Mad -> Machamp
= Strong Sad -> Spiritomb
= The Cheat -> Smeargle (Not as a pet to The Cheat due to the Cheat himself ALREADY being a pet; merely as a buddy that helps him improve on animation and art skills.)
= Coach Z -> Garbodor (Perhaps a friendly one that tries to keep Coach Z out of trouble, and understanding that he means well...also perhaps as a friend to help Coach Z with his rapping talent, too.)
= Bubs -> Melmetal (Perhaps Bubs could have discovered him since he was a meltan RIGHT outside his concession stand, when he was eating leftover scrap metal that Bubs was going to bring to a recycling center...only to have him become his assistant that he bonded with, as a buddy!)
= The King of Town -> Guzzlord (Why would I imagine one of this species of legendary pokemon being the King of Town's OWN pokemon?!? Well...probably it's big appetite!)
= The Poopsmith -> ??? (Maybe some kind of fly pokemon that hasn't been officially introduced, yet? Since a lot of such bugs in real life are known for eating "whatsit". Or perhaps some kind of plant pokemon. Who knows?)
= Homsar -> Pecharunt (Among characters that I KNOW are in the main cast? I can EASILY see Homsar being one with a legendary pokemon....and for some reason? I'd imagine Homsar would have the silliest one, yet!)

Supporting characters: (In alphabetical order)
= Crack Stuntman -> Pangoro
= Marshie -> Ninjask & Shedinja
= Mr. Bland -> ???
= Senor Having A Little Trouble -> ???
= The Announcer -> Mr. Rime
= That Little Chef Guy -> Snorlax (With Snorlax having a big appetite? I can imagine one that would be a good culinary arts assistant, to That Little Chef Guy!)
= The Blacksmith -> Heatmor (Fire AND steel type? That sounds like something The Blacksmith would have; even if legendary!)
= The Goblin -> Hoopa
= The Jibblies Painting -> Darkrai & Cresselia
= The Grape Faerie -> Vespiquen or Beedrill (Probably just being his pet giant bee in an alpha pokemon form.)
= The Knight -> Armarouge & Ceruledge (I imagine BOTH of these particular fire type pokemon being partnered up with The Knight, for obvious "knight" based reasons.)
= The Trumpet Guy -> Wigglytuff (I couldn't think of a more fitting pokemon to be paired with this guy, actually. XD)