Berserk is kinda set in medieval times, so is KonoSuba but if you want one that goes back and forth Fate series often jumps from present day to history to explain the past of the “heroes” .
Good amount of Fantasy a little ways in, the classic anime or the movie trilogy are both great. Manga too is great.
Fate series has some characters from medieval times and they fight (somewhat) like they would in medieval times (sword, lance, etc.) and it shows their backstories in that time period.
Vinland saga is an incredibility well researched Story that takes place during the Viking age.
Claymore is really good however it is only about 26 episodes. The manga is really good too .
Japanese medieval: (loosely defined as pre-Tokugawa period) Sword of the Stranger, Hyouge Mono, House of Five Leaves.
There are a lot of fantasy shows with quasi-European medieval settings but there aren't too many that are realistic. Spice and Wolf, as already suggested, is the closest I can think of.
Kemono no Souja Erin is set in a fantasy world but it is more or less medieval and is a fantastic show.
Most people don't know about it, especially since it turned to crap after the 30th-40th episode, but I rather enjoyed Rouroni Kenshin: tales of meiji .
{Kingdom} wasn't too bad, if you manage to put up with the ugly CGI.
It improves though, or maybe you just get used to it anyway, it's set in medieval China.
European Medieval, oen that hasn't been listed here yet is Record of Lodoss War. It's a 1990 OVA from Madhouse that looks like it's from the late 90s and it's very DnD-esque.
