You can buy yubikeys that aren't attached to a specific service, but that can't be done with the Mt. Gox specific yubikeys.

I've a regular Yubikey (as well as a free Mt.Goxxed one) that I got with a Lasspass Pro package, seems it's an open one & any site that wishes to contract Yubikey's service & not order proprietary keys could easily add this double authorisation to their sites, then if you have a Yubikey you just get the site to recognise it (2 seconds) & that's it - wish my banks would do this (will ask them) & Gmail too (even though they have phone DA) because I like the physical key & change phones (sim cards/numbers) when I travel

Mt. Gox must have the single-slot Yubikey, because I don't see how it would be possible to use both slots for a single authentication.  That's too bad, since many services offer the dual slot version of Yubikey, which gives users an extra slot to use for their own purposes.

We prevent use of the yubikey on other sites to limit (slightly) risks of phishing. Making it normal to enter your yubikey code on other sites might be a risk, and considering recent phishing attempts I wouldn't be surprised we start seeing phishing attempts targetting yubikeys.