They made the sidewalks like that here in Arlington, Va (pavers), only they never seemed to be able to figure out how to keep the pavers from settling and becoming uneven which drew complaints - largely from the elderly and disabled.  I think one of the benefits was also that the pavers allowed rainwater penetration and reduce impervious surface runoff.  However, due to the settling problem, they started putting down a concrete foundation for the pavers which of course eliminated the water penetration and made the construction cost a lot. Now, we are going back to simple poured concrete.      
I have wondered about that in general, since the idea works so poorly in America, and here are a couple of general theories -

  1. The weather is more extreme, especially in terms of water/ice. European weather is more temperate (boring) than the weather I grew up with in Northern Virginia.

  2. The Germans do a much better job building this way. For example, a good number of Aldi parking lots here are made like this, and even after years of cars and the regular 18 wheel delivery trucks, the parking lot is still in fine shape. The various brick shapes, tools, equipment (compacting the soil and sand especially), training, etc. are well tested in practice.

  3. Unlike in America, the German emphasis tends to be on the long term - in other words, the job is done right since it is supposed to last, not merely save money or be attractive. This also includes maintenance.

Personally, it is a good bet that the weather is a solid reason for the difference, but the other two factors also play a major role. All the work I have seen in America wouldn't be acceptable here for even the most casually done homeowner job.
To add to this I understand the Germans include maintenance as a part of the state bid process.  This is where real money can be made.  If you are bidding a project and screw up the maintenance estimate, it's on your company.  If you overestimate what it will cost and you make some extra cash, it's yours - you did a hellavu job!  I like this a lot!
Weather might be an issue, skilled labor certainly, and attitude (long term vs short) - I think you hit them all.

Although I have been to other European cities (not German) where they had pavers hundreds of years old, only they did have slight uneveness to them.  This is one of the reasons that sturdy walking shoes are helpful.  We now adhere to ADA (American with Disabilities Act) that I think requires a certain smoothness to all surfaces and it was this requirement also that I think drove Arlington to go back to concrete.  

Certainly there is a lot of variation between recently laid, consistently produced bricks and things done hundreds of years of ago - there is a lot of variation in Germany too.

But with some experience in pushing people in wheelchairs here, I can say that the German sidewalks definitely stand up well to comparison.

It also occurs to that Germans use fairly heavy and largish bricks in general, while the stones I have seen in American are quite small.

There is a German company, Uni (or Uni-eco) that has patented a paver with a small spacer that leaves a gap between laid pavers, to allow more water to infiltrate into the soil. Neat idea, they are sold worldwide now I believe.
The key with pavers and indeed any pavement is the base. I think inproper base preparation is often the reason you see them fail.
They are going down my street now and tearing up and repouring 5-20 foot lengths of concrete sidewalk where the sections have heaved, mostly due to tree roots.
<q>there is a lot of variation in Germany too</q> You can say that again. The roads and bikeways in Kreis Koblenz are mostly awful for a road bike compared to the roads in Niedersachsen (or for that matter southwestern Indiana).