SSLv2 has been long retired. Last year, SSLv3 was taken out behind the shed and shortly afterward a single gun shot was heard. Being that SSLv3 ciphers persist into TLSv1, it, too, is protocol non-grata. Of those cipher suites in SSLv3, the "strongest," 3DES-SHA and RC4-SHA, have exploitable vulnerabilities in the CBC implementations, ignoring that RC4 is very broken. The same goes for AES-SHA in TLSv1.
The SHA (SHA1) hash, while not yet cracked, has been shown to have weaknesses which could be exploited using available cloud-computing power very very soon, if not already. Thus, certificates are now being issued with SHA-256 (SHA2) hashes.
As of 01-Jan-2016, industry leaders will be making several changes:
1) TLSv1 will be deprecated as a protocol
2) RC4 ciphers will be eliminated
3) SHA1-hased certificates will no longer be issued, the last of which can be issued will expire 31-Dec-2016
The end result is some products produced as recently as 2009 will no longer be able to communicate securely on the Internet (including, sadly and already, my beloved phone.) I believe Amiga SSL implementations for browsing, email, etc. to be even older than that.
TL;DR what is the current landscape of TLS security for the Amiga, and more specifically for Classic 68k? In essence, as of 01-Jan-2016 only TLSv1.2 will be supported by the biggest players in the world. Anyone lagging behind will essentially be forced offline as unable to communicate with the rest of the world securely, and eventually at all as more providers follow CloudFlare's lead in giving free certificates and forcing sites to https. What are our options right now or coming for the Amiga?
