Ougenweide [0] was one of the earliest in the 70ies, Zupfgeigenhansel [1] from the same time did some covers (Bella Ciao in German here)
Die Streuner [2] are not as close to the pure-medieval style but use a lot of self-built instruments.
Satolstelamanderfanz [3] are mostly instrumental and traditional, Corvus Corax [4] are similar, but far bigger, drum heavier, and also have a few covers.
Tanzwut [5] is an example of medieval electro-metal
Schelmish [6] is party-medieval music with metal influences, In Extremo [7] is probably the most successful medieval metal band.
I could probably go on for hours, but I think this is already a bit much, so I’ll stop here ;)
[0]: https://www.youtube.com/watch?v=95EoHfFGBeU
[1]: https://www.youtube.com/watch?v=4_loaZEwKkc
[2]: https://www.youtube.com/watch?v=hOoIHHwjg-0
[3]: https://www.youtube.com/watch?v=ZTJkp06x7EE
[4]: https://www.youtube.com/watch?v=EWruBwPNBOs
[5]: https://www.youtube.com/watch?v=a5fmbSnVQrI