Any Views on What Would Happen to European Travel if the EU Breaks Up?

I'm still hoping that the other countries in the E.U. will agree to the changes, and that another agreement can be reached. As Chani mentioned, collapse of the Euro will have far reaching implications for the world economy. I think it's too early to speculate on "what would happen to European travel", so I'll assess the options according to the current circumstances when I plan my next trip.

I tend to worry only about things I can control. This is not one of them. It would depend on the degree of breakup. Everyone returns to their currency? Difficult and would take time to crank of printing presses, etc. Would border control return? Probably not since the EU and Schengen agreement are not the same. The greater impact would be on the world economy and that could be significant as related to credit markets. It is speculation at the highest level.

What would happen to the currency or the effect on tourism is minor compared to the effect on the world economy, IMHO.

I don't think disintegration is going to happen. There are far too many advantages in the Union to return to the old ways. That doesn't mean there are not problems, of course, and the current problems are inextricably tied to the common currency (the Euro). As others have said, the biggest impact would be on the world economy (just watch how reactive the US (and others) stock market is to any news on the EU debt issue; even good news, such as the recent announcement of upcoming talks where solutions will be sought pushes the markets down because the markets fear the worst outcome). We, and many others throughout the world, would feel that impact. That aside, I think the first thing to go within the EU would be the common currency. For us travellers, that would mean a return to the old days where we changed currency at every border and lose some money in each exchange. Not fatal. Today's Wall Street Journal says that some countries are already starting to print their own (presumably former) currency just in case. Economies of member states would be affected, for sure. Each country that....uh...."overspent" in recent years would have to dig themselves out, and that could be ugly. It shouldn't affect travel between countries, unless the Schengen Agreement was also dissolved. But the Schengen Agreement does not depend on a European Union so it could continue as long as member countries want to participate. Of course, there are many Eurosceptics within the EU who would be thrilled if the EU collapsed. Just my uneducated $0.02.

The only currency of resort would be the dollar; the Renmenbi wouldn't be trusted due to possible manipulation and lack of enforceable contracts. During the interim the dollar would strengthen immeasurably. So, for a change everything would be cheap for us. If we still have jobs. And if airlines are still in business. And ...

There seem to be two choices, either much stronger central government to enforce austerity as the price for staying on the Euro or the weaker countries will return to their previous currencies. I'm really surprised at Germany's patience, first propping up the former East Germany for ten plus years, now propping up other weak countries that refuse to manage their own budgets. I don't expect the trade or Schengen visa free agreements would go away, they've been pretty successful. It's not necessarily a bad thing. Some countries shouldn't have a strong currency. Weaker currency value makes a country's exports and tourism more attractive.