Des réponses à une question que je me posais :

I assume you're talking about SSL/TLS or a similar protocol. In these protocols there are two reasons to use Diffie-Hellman:

Your certificate only supports signing
Either it is an RSA certificate restricted to signing, or it uses an algorithm that doesn't support encryption, such as DSA or ECDSA.
Forward security - What happens if the server's private key gets leaked somehow?
If you simply encrypted the session key to the server's public key, all past communication with that server can be decrypted. Which is very bad.
If an ephemeral Diffie-Hellman key-exchange was used, a private key leak won't compromize past communications, since the keys used for the key exchange are long gone, and the leaked long term key was only used for authentication and not for confidentiality.
You don't know the public key of the other side
There are situations where you don't know the other side's public key, but you have a different way to authenticate them. In that case you can use anonymous Diffie-Hellman together with that other way. For example TLS supports authentication based on a symmetric shared secret in a way that's secure against MitM.

Some other protocols such as CurveCP use EC Diffie-Hellman for both authentication and key-exchange. In this case they profit from the performance advantage elliptic curves have over RSA.

Article anglais encore une fois bien meilleur/complet que l'article français sur DH

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