The WebDAV methods supported by servers include:
1. GET: Used to retrieve a resource identified by a URL.
2. PUT: Used to upload a resource to a server.
3. DELETE: Used to remove a resource from a server.
4. PROPFIND: Used to retrieve properties of a resource identified by a URL.
5. PROPPATCH: Used to modify the properties of a resource identified by a URL.
6. MKCOL: Used to create a new collection resource (folder) on a server.
7. MOVE: Used to move a resource from one location to another on a server.
8. COPY: Used to copy a resource from one location to another on a server.
9. LOCK: Used to lock a resource for exclusive access.
10. UNLOCK: Used to unlock a resource that was previously locked.