I'm far from being an automotive expert but I did have the luxury of driving a lot of different foreign and domestic cars over the three years I worked as a car jockey at a rental company.
In terms of the big three here's what I've taken away with.
Ford: Their current line of cars are solid and reliable as any Japanese car. Their trucks (including SUVs) on the other hand still have issues, but are improving. Most of Ford's current domestic line are in fact European cars. They just put bigger engines in them for the North American market.
GM: Their line of trucks such as the Silverado and Savana are rock solid vehicles. Virtually indestructible. Their cars however still have a lot of quality issues that date back over a decade. GM likes to use a lot of cheap material to cut costs and their cars show it. The Cruze/Cobalt/Cavalier still has that lower control arm issue apparently. Malibus never stay in tune.
Chrysler still has major quality issues across the board with their vehicles. They're unreliable and often require costly repairs. Transmissions still being the biggest problem. I'd hesitate to call them a domestic automaker anymore since Fiat SpA has majority ownership. The advantage here is that Fiat has a strong automotive pedigree to tap into, such as Ferrari, Maserati, Alfa Romeo, and Lancia. The Multiair is a solid engine and 500s are flying off the lot. Fiat has started to shed its "Fix it again Tony" reputation, and that will help Chrysler/Dodge/Jeep a lot. Maybe they'll start actually making cars people want to buy. They would have gone out of business ages ago if it hadn't been for the Caravan.
Japanese cars I find to be pretty consistent quality wise across the board. They're solid built with no major issues. Toyota had a bad patch a couple years ago, but the media blew it way out of proportion.
Korean car makers Kia and Hyundai have improved quality dramatically over the years. Hyundai is as good as the Japanese automakers now. Kias still have their quirks but are getting better.
For German cars, Mercedes and BMW are both solid performers. Volkswagen on the other hand has a lot of mechanical issues. It's a popular pass time for car guys to pick on VW but it's not wholly undeserved. VW and Audi are notorious for electrical problems.
I can't really comment on the French, Indian, or Chinese automakers since the don't sell in North America. Citroen and Renault seem to be doing some interesting things but I can't speak about their quality.