Not really a mascot, but I've had 2 things in my cars over the years.
One was a little guardian angel visor pin that my mother gave me when I first started driving. It just reads "Son, please drive safely." It gets clipped to the visor of whatever car I happen to be driving, and its been on everything I've owned at some point.
The other is this red (more pink now, due to the sun, used to be deep red like Mouse'* car), Koosh ball. I got this thing back in my high school days, and my small group of friends would pass it around during classes, even chucking it out into the hallways to other friends. My best girl friend and I would constantly toss it to each other in between classes as a good luck charm for tests, or tough classes, or whatever. At the end of the day, the Koosh ball would wind up from either of the two of us, sitting on the dash of my 87, where we would pick it up from the next morning when I drove to school.
Its a bit bleached, dry rotted a bit, but still kickin. Been along for the ride in every car I've owned as well. I did take it out when I had to get my inspection done (since we stick the inspection and registration stickers up on the glass, where this guy usually sat behind my GPS). Gotta remember to put the thing back in there! Considering the thing is pushing 17 years old, that'* not bad for a little toy that got kicked and tossed around most of its life. Never had any "official" name, just got called "the red one" or the "red Koosh", or in the case of someone in the hall, they'd peek in the door and ask if I had "it" and I'd chuck it out to them.