The OPERA superluminal neutrinos were shown to be an artifact of a clock synchronization error. As such, the only appropriate answer to this question would be simply: no.
Not only are neutrinos not superluminal, but because evidently neutrino oscillation can happen as a result of interaction with the electroweak, the neutrino might actually get its tiny mass from the Higgs mechanism. The Higgs mechanism is what prevents a lot of particles from going superluminal; not just the neutrino.
Answers associated with the OPERA superluminal neutrino fiasco that do not venture to explain how it went wrong are unhelpful to anyone not interested in anything but a historical record of a major league physics embarrassment.
If I didn't already know better, I'd be pretty confused by these answers. An awful lot of them are by people with much stronger reputations here than mine. Please give me enough points for several dozen down votes, and I'll see if I can help to remedy the situation.