Do I need research experience to be admitted to a highly ranked mathematical physics master's? I am a third year student doing my bachelors in both physics and mathematics at a German university. Since I am really interested in theoretical physics and mathematics I am thinking about doing a masters degree in mathematical physics. I am very interested in Mathematical Quantum Mechanics and, even though I haven't had courses in it yet, in QFT and General Relativity.

I'm thinking about applying for Part III of the Mathematical Tripos in Cambridge. It's probably quite hard for a German student to get accepted in Cambridge, isn't it? So my question is:

Do I need research experience, papers or something like that? At German universities we don't really do research or write papers in the bachelor studies of theoretical physics or mathematics (apart from the bachelor thesis itself).
Having research experience will certainly help your application to an elite program.  However, it is definitely not a necessity.  Moreover, the graduate faculty at top institutions are used to fielding applications from all over the globe; they should be reasonably familiar with what kind of preparation students from Germany will typically have.

However, if you are serious about pursuing graduate studies, only applying to a small number of top programs is not usually a good approach.  The top programs frequently need to reject a significant number of totally qualified applicants, simply because their space is limited.  I would suggest that you apply more broadly if you want to ensure that you can get into a top program.