I got myself a nice security key (Yubico Fido) today, which utilises the U2F protocol. But to my surprise not a single Bitcoin exchange seems to support this yet, only Google itself.
So which Bitcoin exchanges (plan to) support U2F?
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As you have correctly noticed none of the Bitcoin exchanges have implemented the FIDO standards there is not a large demand for this feature from what I gather. If the standard were to gain mass adoption and many users began requesting it I'm sure it would become a greater priority for exchanges to implement.
As a side note the Ledger hardware wallet does support the U2F standard and would be a great way to improve the security of your wallet (as long as you don't connect the two to each other (i.e. same keychain)).
See headline Cryptocurrencies on http://www.dongleauth.info/#bitcoin for a list and some buttons to push and presumably help speeding up implementation.
Your Yubikey Fido, and other cheaper keys like ePass and HappLink (formerly pu1.fr) also only support U2F, so any support for OTP is less interesting in this context.
And as Mark S. writes, currently none are listed as supporting U2F.