Having an active Familiar can spare you death by overload. Possibly death in general, but it's not something I've tested (nor plan to). Saving your sim from death has a one week cooldown, or at least so I've read. Again, Haven't had a chance to test, don't plan to.
They also seem to help when studying magic and with keeping charge manageable. Both are passive effects, so I'm just going based on observation.
Cat and dog familiars can also go scavenge for spell ingredients, brooms, or wands.
The orb ones don't do much, true, but some of their quips when you brew a potion or learn a new spell can be cute/funny. And they seem to have different personalities, and not necessarily based on what type of familiar they are.