The TLS ECDHE cipher suites are not simply "Elliptic Curve Diffie-Hellman key exchange"; that would also include the ECDH cipher suites. The ECDHE ones use ephemeral ECDH keys rather than fixed ones (which is what the ECDH suites use). See RFC 4492, among other references. The ECDH suites do not provide PFS.
As codebeard noted above, DHE and ECDHE can be used with RSA keys. The alternatives are DSA and ECDSA keys; if you include ADH and AECDH key exchange, you can also use no asymmetric key pair for authentication, though in that case you have no way in the protocol of verifying the peer's identity.
Key exchange and peer authentication are two different aspects of SSL/TLS, and RSA remains the most popular alternative for the latter. RSA keys aren't going anywhere.