How do I list the SSL/TLS cipher suites a particular website offers?

I wrote a bash script to test cipher suites. It gets a list of supported cipher suites from OpenSSL and tries to connect using each one. If the handshake is successful, it prints YES. If the handshake isn't successful, it prints NO, followed by the OpenSSL error text.

#!/usr/bin/env bash

# OpenSSL requires the port number.
SERVER=$1
DELAY=1
ciphers=$(openssl ciphers 'ALL:eNULL' | sed -e 's/:/ /g')

echo Obtaining cipher list from $(openssl version).

for cipher in ${ciphers[@]}
do
echo -n Testing $cipher...
result=$(echo -n | openssl s_client -cipher "$cipher" -connect $SERVER 2>&1)
if [[ "$result" =~ ":error:" ]] ; then
  error=$(echo -n $result | cut -d':' -f6)
  echo NO \($error\)
else
  if [[ "$result" =~ "Cipher is ${cipher}" || "$result" =~ "Cipher    :" ]] ; then
    echo YES
  else
    echo UNKNOWN RESPONSE
    echo $result
  fi
fi
sleep $DELAY
done

Here's sample output showing 3 unsupported ciphers, and 1 supported cipher:

[@linux ~]$ ./test_ciphers 192.168.1.11:443
Obtaining cipher list from OpenSSL 0.9.8k 25 Mar 2009.
Testing ADH-AES256-SHA...NO (sslv3 alert handshake failure)
Testing DHE-RSA-AES256-SHA...NO (sslv3 alert handshake failure)
Testing DHE-DSS-AES256-SHA...NO (sslv3 alert handshake failure)
Testing AES256-SHA...YES

EDIT: Add flexibility as host and port are provided as parameter to the script

Nmap with ssl-enum-ciphers

There is no better or faster way to get a list of available ciphers from a network service. Plus, nmap will provide a strength rating of strong, weak, or unknown for each available cipher.

First, download the ssl-enum-ciphers.nse nmap script (explanation here). Then from the same directory as the script, run nmap as follows:

List ciphers supported by an HTTP server

$ nmap --script ssl-enum-ciphers -p 443 www.example.com

List ciphers supported by an IMAP server

$ nmap --script ssl-enum-ciphers -p 993 mail.example.com

Here is a snippet of output from a Dovecot IMAP server:

993/tcp open  imaps
| ssl-enum-ciphers:
|   SSLv3:
|     ciphers:
|       TLS_DHE_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_RSA_WITH_IDEA_CBC_SHA - weak
...
|   TLSv1.0:
|     ciphers:
|       TLS_DHE_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_RSA_WITH_IDEA_CBC_SHA - weak
...
|_  least strength: weak

Nmap done: 1 IP address (1 host up) scanned in 1.03 seconds

Is there a tool that can test what SSL/TLS cipher suites a particular website offers?

Yes, you could use the online tool on SSL Labs' website to query the Public SSL Server Database.

Here is a snippet of information that it provides:

(screenshot from results of google.com)