Can i authenticate myself in SSL with a key, just like in SSH?
SSL/TLS supports authentication of the client with an asymmetric key pair. Since this is SSL, it takes the form of a client certificate. The server requests a certificate during the initial handshake, indicating which root CA the server will use to validate that certificate; the client then sends a certificate to the server. This of course requires the client to actually have a certificate to send.
Usual clients (browsers) and servers support this feature. What the server does with the certificate is entirely up to it. In a Microsoft Active Directory + IIS world, the client certificate, once validated, is mapped to an account through one of several mechanisms (either the certificate itself is already attached to the account in the AD server, or the account name is found as a "User Principal Name" in the client certificate).
@Rook talks about TLS with SRP, which is something completely different: with SRP, client and certificate authenticate each other with a shared secret (a password). There is no certificate anymore, not in the client and neither in the server. This has no equivalent in SSH (there was a patch to SSH for that, but it is not much maintained; it does not map well to account names and authentication as they are usually managed in operating systems). Usual SSL clients and server do not support SRP (but this may come in the future).