Amidst the financial-world fallout, if haven-seeking investors rush into the Yen and push it back down under 100 to the USD, I would not be surprised to see the Japanese government take extreme measures to weaken it, including the pouring of fresh Yen directly onto the FX market. That'll be fun.
Anyway, at its most boring, the brexit could result in the UK and the EU doing what they've always done, just with lots of time and effort spent to put it under a different banner.
At its most dramatic, it could result in the breakup of the UK and a major compromise in the stability of the EU.
Whatever happens, there will probably be some lessons for the 21st century in this. Now that the decision has been made, here's hoping it winds up being good for everyone, I guess.
EDIT: In the news, there was a lot of emphasis on the fact that many Japanese companies had chosen the UK as a hub of manufacturing for goods to be sold throughout the EU. Naturally, the reason to manufacture within the UK was to avoid EU tariffs, but this (probably?) threatens all of that.
If I were Scotland and thinking about splitting off from the UK to rejoin the EU, I would be courting the heck out of companies in this kind of position. It's probably far easier for them to just move up north a little bit than it is to move to somewhere more profoundly different, and in the case of firms from Japan and other East-Asian countries, their overseas staffs would almost certainly prefer to live and work in English.