HTTP Basic Auth
1) HTTP Basic Auth sends passwords over plaintext. (Digest Auth at least hashes passwords, but isn't a huge security win either.)
2) Basic Auth still requires user management and if you are going to build a user management database you might as well build a login flow in HTML instead of basic auth (not just because basic auth is ugly but because you can own that login flow and provide handy things like password recovery which basic auth doesn't support).
As pointed out elsewhere, HTTPS Client Certificates are a much better option baked into every browser, but we've never figured out the UX to make it convenient for the average user.