I honestly give it about a 70/30. 70% it survive with no (or possibly minimal) interference / 30% try to actively suspend or stop transactions with crypto. I put this over a 5 year timeline, since, now that crypto is really entering the mainstream consciousness, governments will eventually be cornered to make up their minds about what they'll allow (until the last year, many of them treated this sector as a novelty, but with bitcoin's massive swings and the ICO craze, they can't avoid the topic much longer). I think it'll still take 5 years because governments are generally pretty slow, and they'll form "special investigative committees" and other things which usually operate on a 1-2 year timeline themselves. In either case, I'm really referring to the exchanges, since this is really the only place that governments can effectively interfere if they decide to. The biggest issue will be whether or not so-called old money (banking/finance/wall street) feels like its being left out or not. If they think they can make money on this, then it'll survive. If not, they'll exaggerate money laundering, terrorists financing, or they'll wait for a big loss to take place, and claim that, in the name of protecting people, only "registered" investors with assets totaling X amount should be allowed to invest in crypto. Why I rank this 70/30 is that I think we're beginning to see signs that "old money" does in fact think they can prosper here.
All that said, I don't think the current wild west version of the cryptosphere will continue as its has been, and I do think that more "oversite" will be added which will be annoying (I think ICOs will face more and more scrutiny for instance), but, by and large, I think that crypto will survive.