Well, german states (Bundesland) aren't as independent as american states or Switzerlands cantons. They have no own taxes for instance, taxes are the same in the whole of germany. Many other stuff is central too.

I wanna try too, I lived in Germany 1 year during a school exchange and I think I actually memorized the majority (but not every single) state.

1. Baden-Wuttenberg, Stuttgard -- correct

2. Bayern, München --correct

3. Berlin -- correct (as city state it's capital and the state is the same)

4. Bradenburg + ??? -- the capital is Potsdam, but the state is correct

5. Bremen -- correct, the second city state

6. Hamburg -- correct, and the third city state

7. Kassel? -- Hessen, Wiesbaden; Kassel is a city in Hessen though

8. Macklemburg-Vopormenn -- correct, capital is Schwerin

9. Niedersachsen, Hannover -- correct

10. Nordheim-Westfalen, Bochum? Essen? Dortmund? Dusseldorf? -- Düsseldorf

11. Rhineland -- Rheinland-Pfalz (or Rhineland-Palatine in english), correct, capital is Mainz

12. Saarlandes -- correct, capital is Saarbrücken

13. Sachsen, Dresden -- correct

14. Sachsen-Anhalt -- correct, Magdeburg

15. Don't remember the name exactly, I know it has Holstein or something and the capital is Kiel -- correct, full name is Schleswig-Holstein

16. Turingen -- correct, capital Erfurt

How did I do it? -- very well

I know the 10 Bundesländer of Austria, that's good enough for me. And no, I didn't have to look up a map to count how many Bundesländer Austria has.

EDIT:

Give it a shot if you want. The table has all answers in it, so you can guess your way to victory even if you don't know anything. Bonus points if you know what the piece without a number is.

Try to do Spain's autonomous communities similar to the NA states:

Semi-serious attempt:

Edit: I forgot 17 - the Canary Islands