An attack affectionately known as "POODLE" (Padding Oracle On Downgraded Legacy Encryption), should put a stake in the heart of SSL, and move the world forward to TLS. There are two interesting vulnerabilities: POODLE, and the SSL/TLS versioning fallback mechanism. Both of these vulnerabilities are discussed in detail in the initial disclosure.
POODLE is a chosen-plaintext attack similar in effect to BREACH; an adversary who can trigger requests from an end user can extract secrets from the sessions (in this case, encrypted cookie values). This happens because the padding on SSLv3 block ciphers (to fill out a request to a full block size) is not verifiable - it isn't covered by the message authentication code. This allows an adversary to alter the final block in ways that will slowly leak information (based on whether their alteration survives verification or not, leaking information about *which* bytes are interesting). Thomas Pornin independently discovered this, and published at StackExchange.
On its own, POODLE merely makes certain cipher choices no longer as trustworthy. Unfortunately, these were the last ciphers that were even moderately trustworthy - the other ciphers available in SSLv3 having fallen into untrustworthiness due to insufficient key size (RC2, DES, Export ciphers); cryptanalytic attacks (RC4); or a lack of browser support (RC2, SEED, Camellia). The POODLE attack takes out the remaining two (3DES and AES) as trustworthy (and covers SEED and Camellia as well, so we can't advocate for those).
One simple answer is for all systems to stop using these cipher suites, effectively deprecating SSLv3. Unfortunately, it isn't that easy - there are both clients and servers on the Internet that still don't support the TLS protocols or ciphersuites. To support talking to these legacy systems, an entity may not be able to just disable SSLv3; instead they'd like to be able to talk SSLv3 with those that only support SSLv3, but ensure that they're using the best available TLS version. And that's where the next vulnerability lies.
SSL/TLS Version Selection Fallback
We've probably all encountered - either in real life or in fiction - two strangers attempting to find a common language in which to communicate. Each one proposes a language, hoping to get a response, and, if they fail, they move on to the next. Historically, SSL/TLS protocol version selection behaved that way - a client would suggest the best protocol it could; but if it had an error - even as simple as dropped packets - it would try again, with the next best version. And then the next best ... until it got to a pretty bad version state.
This is a problem if there's an adversary in the middle, who doesn't want you picking that "best" language, but would much prefer that you pick something that they can break (and we now know that since all of the ciphers available in SSLv3 are breakable, merely getting down to SSLv3 is sufficient). All the adversary has to do is to block all negotiations until the client and server drop down to a SSLv3.
There is a quick fix, to merely disable SSLv3. This means that if an adversary succeeds at dropping down, the connection will fail - the server will think it's talking to a legacy client, and refuse the connection. But that's merely a solution for the short term problem of POODLE, because there are other reasons an adversary might want to trigger protocol version downgrade today (e.g., to eliminate TLS extensions) or in the future (when TLS1.0 ciphers are all broken). A longer term fix is the TLS Signaling Cipher Suite Value (SCSV). This is a new "cipher suite," that encodes the best protocol version that the client would have liked to use. This is carried as a new cipher suite; servers that support SCSV don't actually treat it as a cipher to choose from (what cipher suites normally list), instead, if the value carried in the SCSV is *worse* than the best protocol version that the server supports, it treats this connection as one that has been attacked, and fails the connection. A client only sends an SCSV value if it has already been forced to version downgrade; it's a way of signaling "I tried to connect with a better protocol than I think you support; if you did support it, then somebody is messing with us."
So POODLE should put a stake most of the way through SSL's heart, and SCSV will help us keep it there. Long live TLS.