For years, we had mostly german and french cars, then some soviet, czechoslovakian, east german and even polish (although those were an exchange between Zastava and Polski Fiat), and then the domestic production, under licence of Fiat (Zastava in Kragujevac), Renault (IMV in Slovenia), Citroen (Cimos/Tomos in Koper, Slovenia) and VW (Vogošća, near Sarajevo). There were some brief runs of other models (like Opel in Kikinda).
What Zastava sold as their own models are mostly reworks of Fiat's - Zastava 101 (aka kec) of model 128, by converting the sedan into a hatchback. The Yugo, which was touted as an all-domestic model is actually based on the model 127, it's the body that was all new but also done by italian designers (nobody complained, they were still the best). Yugo Florida, the last model in the series, is probably the only one designed in Kragujevac.
That story ends in the eighties. Then throughout the nineties the domestic production dwindled to a trickle, along with destruction of the country and its industry. Zastava kept making various brands of Yugos, but with lots of trouble in production, as most of the parts manufacturers were now in suddenly foreign countries. They more or less managed to substitute that with imports from Fiat or from local manufacturers, and the mileage did vary. Yugo could be a good car, if you were lucky.
By late nineties, the average age of a car in traffic was about 13 years. The replacement of clunkers with newer cars took a decade, and some of the oldtimers are still around - you can still see many of the Lada, fića, VW Golf 2 (favorite bosnian car forever), and even an occasional Citroen 2CV. Now Zastava is churning lots of Punto, and it seems to be the single most numerous car around. Most of the cars are still such smaller models, but then there are also all kinds of cars - several japanese brands, two or three korean, the usual french trio (Renault, Citroen, Peugeot) and a bunch of german ones (mostly VW, but Opel is still popular, beemers and audis too). There's even one small model of Chevrolet that's become popular, and Smart is just as frequent as anywhere, i.e. if you drive around you'll probably see one.
Interestingly, the romanian Dacia seems to sell well. Back when they started making Renault 12, I was surprised how they managed to turn an elegant car into something ugly, using the same presses.
Special note: manual gear shift prevails. Actually, I don't remember seeing an automatic sold here, but then I'm not exactly up to date with what sells now. I just don't know anyone who has one.