Same in Switzerland. If they don't want you working for someone else, they have to keep paying you.

The only "non-compete" clauses that are even theoretically binding apply to stealing clients andn customers and the like so generally only apply to sales people.

This doesn't stop companies trying to include ridiculous non-compete clauses in employment contracts. It's sort of a silly pretence - both sides know it's not binding so the employer makes it sound as harsh as possible but the employee signs anyway.

At the end of your employment (whether fired or you walk), if they really want you to not complete, they have to offer you money - generally fully salary for the desired period of time regardless of what your contract states.

That's a year I could spend doing SICP exercises and learning to program in brainfuck. Of course, I would happily turn these projects over to the company and do so with an air of personal superiority regarding my work. And also pick up my paycheck.

That sounds very reasonable. And to take it a step further, if they want possession of ideas you have in your spare time, then they should pay for your spare time too! :)

Well, that's the basic idea behind being salaried. Theoretically you are not being paid for 40-hours a week, you're being paid for your productive output regardless of the time.

What if you work part-time? And spend your spare time on a side-project? Will they pay for it?

That's pretty interesting.

Do you think someone in Germany under such an agreement could work for another company that had no presence in Germany or, perhaps, the EU?

That would be fine because that someone would not be a competitor of the company. Although you have to consider that if you earn money while being paid through such an agreement your earnings are partly deducted from them. So if you find a job which pays the same as before, your old company will only need to pay until your income reaches 110%(125% if you moved for your new job) of your old income. You are also not allowed to "maliciously refrain" from working in that time. (But that is interpreted quite lax for the employee)

Spend the year taking classes, learning new programming languages and tools. There are ways to make it work for you.