1965-67 Rambler Marlin. AMC's flop fastback. Mitt Romney used to have one! Such a weird and wonderful looking car. The Javelin today is more popular and was more powerful, but the Marlin's design has aged better.
Studebaker Hawk (any model). Actually, any Studebaker would do, including the bullet-nosed Commander.The first time I saw a Silver Hawk, I literally gasped. So, so beautiful.
BMW Isetta (any year). Are you noticing a trend here? Yes, I like weird looking cars. The Isetta must be one of the most bizarre, impractical, and probably crazily dangerous vehicles ever made. I used to see a fair number of these around in Tucson; there must have been a collectors' club or something.
1961 Dodge Polara. Features the most beautiful back-end treatment of any car I've ever seen. Plus, you could get it with an optional 45 record player! Early 60s Chrysler products were gorgeous, much lovelier than anything Chevy or Ford produced. Later Polara models were incredibly ugly.
1960 Plymouth Valiant. OMG, so cute with its vaguely insect-like look and adorable spare tire articulation on the trunk cover. See what I mean about early 60s Chrysler designs?
1961-1964 Volkswagen Karmann Ghia. My first car was a bright yellow 1964 KG, and it was so much fun to drive, like a Beetle with all the design flaws removed. Mine eventually got into an argument (not my fault!) with a 1969 Ford Galaxy and guess who won? My next car was a '72 model, not as nice, and it burned to the ground almost instantly. :(
AMC Gremlin (all models). Joke all you want, but I think these are really cool looking cars, and with each passing year, they appear more exotic. I went to a car show in about 1997, and the biggest crowds were ogling the tricked-out, customized Gremlins and Pacers, and they were SUPERB.
There are many other cars I love, but I generally don't care for 50s cars or anything at all past 1980, unless it's, you know, a Rolls Royce (I've driven one; it's like steering a cloud) or something.
What's your favorite?