SSLv3 is Broken
With the advent of POODLE, all the cipher suites used by SSLv3 have been compromised, and the protocol should be considered irreparably broken.
You can check if your website is available over SSLv3 with
curl -v -3 -X HEAD https://www.example.com
-v argument turns on verbose output,
-3 forces curl to use SSLv3, and the
-X HEAD limits the output on a successful connection.
If you are not vulnerable, you should not be able to connect, and your output should look something like this:
* SSL peer handshake failed, the server most likely requires a client certificate to connect
If you are vulnerable, you should see normal connection output, including the line:
* SSL 3.0 connection using SSL_NULL_WITH_NULL_NULL
It's not just websites that are available over SSL. Mail, irc, and LDAP are three examples of services available via secured connections, and are similarly vulnerable to POODLE when they accept SSLv3 connections.
To connect to a service using SSLv3, you can use the
openssl s_client -connect imap.example.com:993 -ssl3 < /dev/null
-connect argument takes a
hostname:port parameter, the
-ssl3 argument limits the protocol versions negotiated to SSLv3, and piping in
STDIN immediately terminates the connection after opening it.
If you connect successfully, SSLv3 is enabled; if you get a
ssl handshake failure then it is not.
There is an excellent question and answer on the Security SE: https://security.stackexchange.com/questions/70719/ssl3-poodle-vulnerability