SSL has been replaced by TLS 1.0 as the current HTTPS standard. It is possible in many browsers to select which SSL and TLS versions are enabled. Any browser you use should support TLS and offer it by default to HTTPS-protected Web sites. Most browsers still support SSL Version 3.0, which is next closest in strength to TLS, and many browsers continue to support SSL Version 2.0, but may have it disabled by default. SSL Version 1.0 is considered insecure today, although some browsers still use it.
CiphersCommon TLS/SSL symmetric ciphers, in order of strongest to weakest (generally), include Advanced Encryption Standard (AES), Triple DES (3DES), RC4, Data Encryption Standard (DES), and RC2. Every browser today should be offering AES as its default symmetric protocol, followed by 3DES as a backup. The other protocols should only be used for legacy compatibility or offered last.
Common TLS/SSL asymmetric ciphers, in order of strongest to weakest (generally), include Elliptical Curve Cryptography (ECC), Rivest Shamir Adleman (RSA), and Diffie Hellman (DH, or DHE for key exchange). ECC is the newly crowned standard for asymmetric ciphers these days, and it's included in the U.S. government's Federal Processing Information Standards (FIPS) as part of what is called Suite B. A browser must support Suite B to be considered for use by the U.S. government. Browsers should offer ECC as the first asymmetric cipher, followed by RSA or DH.
Common cryptographic hash functions include, in order of strongest to weakest (generally), SHA-512, SHA-384, SHA-256, SHA-1, and MD5. MD5 and SHA-1, by far the most popular hashes used, have been shown to have some moderate cryptographic weaknesses, and therefore crypto experts recommend stronger hashes. Of the two, MD5 has been demonstrated to have larger vulnerabilities. Recently, it was shown that digital certificates signed using MD5 hashes cannot be relied upon. Users should avoid cryptography employing MD5 and strive to implement SHA-2 (the family of SHA-256, SHA-384, SHA-512) whenever possible.
SSL/TLS symmetric key sizes often range from 40-bit (the old SSL standard) to 512-bit (very strong). Symmetric key sizes of 128-bit to 256-bit are considered secure for most normal security operations, and 256-bit keys are just now becoming the standard, although 128-bit keys are still the most popular.