I've played in a lot of games over the years. In 90% of them, the familiar tends to be an afterthought. They give a bonus and live on a shoulder, in a backpack, etc ...
In those other 10%, they are very useful.
One of my sorcerers has a bat familiar that warns him if anything invisibile approaches. It scouts out natural dungeons, retrieves fallen items in combat and sometimes enters the fringe of the fray after being hit with a polymorph spell so that it can perform some useful, though low risk, activities (such as mending wounds with healing potions, opening doors, searching for stuff, etc ...) It has also done useful things like knock torches off of sconces, chewed through ropes ... and *successfully* bull rushed a kobold off the edge of a bridge.
That bat has a distinct personality akin to secondary characters in a fantasy novel: only a few distinct traits, but those are a bit exagerated.