I loved the His Dark Materials series (golden compass was the first book in USica).
I would love an RPG where PCs have powers, but also have a familiar who also has powers, or is in some way integral to whatever powers the characters have.
Wondering if a) there’s already an RPG for this and b) other media touchstones.
Beyond His Dark Materials, Pokemon also comes to mind (although not exactly what I was thinking). And I guess Codex Alera by Jim Butcher.
Others?
Depends on your definition of familiar…
Cringer could turn into battle cat in masters of the universe 
i’m pretty sure there were feats in Pathfinder that let your familiar take class levels, so you had familiars using poison and sneak attacks 
in the old sabrina tv show the cat could talk, or inspector gadget ‘brain’ the dog perfectly understood english
in penny dreadful, were the scorpions part of vanessa ives? her familiars?
in beastmaster was his hawk and panther his familiars since they could share senses?
Familiars of Terra is exactly this; the His Dark Materials series is actually listed as one of the game’s touchstones along with some others (e.g. Tamora Pierce’s Wild Magic, Digimon and Pokemon):
“a tabletop roleplay game set in Terra, a fantasy world in which every person has an animal familiar. As a heroic Seeker you travel the lands with your familiar healing the devastation of a war which left nations scarred and people scattered…Help restore the land to its former beauty, bond with your familiar and discover your joined destiny.”
The game itself has a really interesting setting. It has fantasy elements with familiars with powers (e.g. your familiar can ghost-phase, teleport, be giant sized, talk, just to name a few), but also has sci-fi elements. The world survived a horrific war with nuclear weapons that mutated and warped parts of the land and wildlife. It includes space for mutant creatures, robots, labratories, and futuristic tech next to more fantasy like elements of people living in cities built into giant trees and ghosts (as a few examples).
The familiars are a huge part of the game: you create your familiar in as much detail as your human character, and can use their skills/powers as much as the human character. Finally, the human character has powers, mostly tied to their reputation which leads to some cool story elements. Like, you can be “Lana the Jubilant” and you gain a skill-check bonus when you try to improve someone’s mood, or “Meira the Reckless” and gain a bonus when you rush into a situation.
That sounds amazing. I’ll have to check it out.
Other media touchstones: Disney “Princess” movies, Harry Potter patronuses.
Like @sjbrown said, Iago from Aladdin might be an ideal familiar template. Probably tone down the attitude tho.
Fawkes the Phoenix is essentially Dumbledore’s familiar in Harry Potter, yes?
I guess there may be a connotational shade between familiar and wizard’s pet, but many creatures that are textually the later can be read as subtextually the former…
See also: Merlin’s owl Archimedes in The Once And Future King (or at least the Disney animated version, The Sword in the Stone).
Perhaps off the beaten path: The Saga comic series by Brian K Vaughan and Fiona Staples. There are bounty hunter characters and each has a giant animal sidekick with a special power. The first one we meet is Lying Cat.
Cursor from TRON.
Bubo the mechanical owl in Clash of Titans
For some non-traditional Familiars.