The first Mazda RX 7 had the shape of the "trochoide" (the "cylinder" of the Wankel-engines) not as a logo, but as a design-element of the wheels:
http://imcdb.org/vehicle_117266-Mazda-RX-7-FB-1981.html

But I think, these wheels were only available in Europe. The most pics of RX 7 in this forum are from US-movies, and there you cannot see these wheels. But in Europe they are still popuplar for RX 7-freaks.

The legendary motorbike Münch TTS ( http://imcdb.org/vehicle_105887-Munch-4-TTS-1200-1971.html ) is always called Münch "Mammut" (mammoth). But the constructor Friedel Münch wasn't allowed to use the name "Mammut". But often a logo with a mammoth-head was mounted on the bikes.

A globe on the 1952-1959 Ford Taunus.

The Chevy Impala also wears a special badge.

I don't mean to offend, but perhaps this is the time that some American car companies were trying to sell cars by patriotism alone? For the record, the bird mascot was an eagle, which, while not the national symbol of the Bald Eagle, still commands some authority in the animal kingdom.

Yes, two things wrong with the re-imaging of Buick during that time. (1) How could the new corporate mascot be so linked to the brand's sub-compact class offering, when the brand had always been known for its large luxury sedans that still have plenty of power? (2) Couldn't they find a more "Regal" name for that bird than "Happy?" I mean, come on!

Two more, though appearing only as decals, not on badges: Dodge Super Bee and Plymouth Roadrunner Superbird

Close up of Superbird rear wing.

Edit: One from US-market,--Mercury Cougar.
See grille emblem:


Another decal-only: Pontaic Firebird

I always liked the manta ray emblem on early Opel Mantas.
And don't forget the Viper's snake head or the Corvette flags.

Never quite understood that Buick "hawk" thing. I have a 1978 Buick full-line sales brochure and that brown hawk is all over it. It just doesn't make sense in my mind why they would want to be represented by a hawk.

The Citroën 2CV had many official special versions, many of which were only locally available. In Germany the 2CV was nicknamed 'Ente' (duck) and probably only a fraction of people that knew the 'Ente' actually knew it was made by Citroën! i remeber two special versions that used the nickname:
The 'Sausss-Ente'


and the 'I fly bleifrei' (bleifrei means lead-free)

To stick with the mountains: Some Jeeps currently wear the "Trail Rated"-Badge