For RSA or DH (not DHE) cipher suites, you just need the server private key, of type RSA or DH, respectively (DH certificates are exceedingly rare).
For DHE cipher suites, you would need the dynamically generated Diffie-Hellman private key. This key is never stored anywhere, and that is by design. Correspondingly, you cannot decrypt the data afterwards. This is called Perfect Forward Secrecy.
For the TLS cipher suite with a pre-shared secret: raw PSK cipher suites can be decrypted with knowledge of the shared secret; RSA_PSK suites need knowledge of both the shared secret and the RSA private key; DHE_PSK suites provide perfect forward secrecy.
SRP cipher suites also provide perfect forward secrecy. There again, this is by design: if knowledge of the password sufficed to decrypt a recorded connection, then this would allow offline dictionary attacks, precisely what SRP is meant to thwart.