FlameBot
First time out of the vault
Also the toaster (from old world blues). I don't think I need to elaborate on that.
Out of the base game companions, the only one I did not like as much as the rest would be Rex (and even he has a special place in my heart with his hatred of rats and hats along with his long history plus Old World Blues even remembered to give him a happy ending). All the companions were great and memorable in their own ways with detailed stories attached to them so I can't pick my absolute favorite from the lot (though Boone, Veronica, Raul and Cass are top contenders).
As for other characters; Joshua Graham, the Think Tank (Mobius included), Vulpes Incula, Elijah, Christine Royce, Ulysses (when he's busy not preaching), Sarah Weintraub, Tabitha, Davison and Mr. House.