The Spanish public has overwhelmingly voted "si" to the EU Constitution in a public referendum. While turnout was low - only 42% - it's still not a bad start for the next stage of European unification. Hopefully the other countries which have scheduled referenda will get this sort of result.
The problem is what happens if they don't. In order to come into effect, the EU COnstitution must be ratified by all 25 member states. And actually, I don't think that's likely. Every country has parties opposed to greater European integration, or nationalist sticking points which stand in the way of ratification - and one of them is almost certain to win some time. What happens then?
The short answer is "nothing" - the process stalls, and Europe continues as it is. But this is unlikely to satisfy the unifiers, and they are likely to seek a way forward for those who want to travel it. The problem is what that way forward would look like, as the natural institutions of governance for a unified Europe - the European Parliament, the Council of Ministers - are already used for governing the not-quite unified Europe, and can't really serve a dual role. Either they'd need to start throwing people out, set up parallel institutions, or find some way of splitting the institutions so that a subset can make decisions which apply only to the unifiers (but then how do they deal with contradictory decisions?)
Ultimately, it's going to come down to numbers. If only one or two nations reject further unification, then they may very well find things going forward without them. If there's a wider rejection, then the whole European project may very well stall for good.