Not all toilets are created equal. Which AS toilet do you have? SOme work fine, then there are others.
I, and a lot of others here, have and like their Toto toilets. I'm not sure they make a dog, but some do perform better than others. If I was going to get one now, depending on the style I was trying to achieve in the bathroom decor, I'd consider the Toto Drake II. I put in two of the original Drakes at my mother's house, and she's not had any problems. I have a Toto Vespin and a Carlyle. Both of those have been updated, but mine work fine.
Terry sells most brands and models, but reports the biggest repeat customers and the highest satisfaction comes from Toto toilets and reports less than 1% defect rates, where some of the others ended up nearly 50% (and he stopped selling them). Check out his toilet recommendations page - real world user evaluation, not lab tests and short-term checkouts.
Toto is the world's largest toilet manufacturer and has a factory in Alabama. Not all of their toilets come from there (they have factories all over), but corporate wide, they have excellent quality control and product design.
There are some people (a small percentage) that have a medical problem and have exceptionally hard and long stools. For those, probably the best toilet is the Caroma brand. These have a 3" trapway. They work, but have other issues. They are the only one made (that I know of) that have a trapway that big in diameter. The vast majority of the population can get along fine with one of the better toilets, and in my eyes, Toto wins for the largest variety in that category.