What is the current status of IPv6 support?
From what I gathered reading the Wiki, protocol specifications support IPv6, but the original client does not.
However, I also came across the description of Bitcoins.lc, who claim "full IPv6 support".
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The standard Bitcoin client does not at this time support IPv6. Bitcoins.lc is a mining pool, and mining pools work by having an interface (such as PushPool) visible to the public which handles all the getwork stuff and various internals, miner tracking etc. This interface operates as a proxy to the actual bitcoin client and so the client itself can bind to an IPv4 address which is local relative to the mining interface which can have full IPv6 support.
In short, it is not the bitcoin client which bitcoins.lc is claiming IPv6 support for, but the proxy to which pooled miners connect.
Edit: It looks like sipa has submitted the necessary code. According to TheBlueMatt, there is "some alternate connection logic and anti-DDoS stuff wrt filling addr.dat on IRC" that needs to be done first. In any case the code is out there so it shouldn't be long now until it finds its way into the official client.
Update: IPv6 support was merged into the mainstream client and should be available in the 0.7.0 build.