Britain voted to leave the European Union as part of the controversial "Brexit" decision. This means that other countries will likely follow suit once they see how Britain functions as a more independent nation. As a result, the European Union won't be able to hold on as an institution for much longer.
The U.K. voting to leave the EU will have some serious consequences for the U.K., the EU and the rest of the world, but it will not be the end of the EU. There will likely be a decline in the power of the EU, but the EU is still strong, and it will survive this issue.
I am sure that UK's separation from the EU will certainly trigger other members of the EU to want to leave as well. However, those countries that have benefited and will continue to benefit from their affiliation to the EU would remain loyal to the union. Attrition always leads to some sort of turmoil, whether minimal or large scale, but each member of the union would have to take a close look at how a separation would affect their nationals and ultimately their nation as a whole.
Though the U.K. voted to leave the EU, however, this will not cause the end of the EU. The EU has definitely lost one of its largest and wealthiest members and this would have serious economic implications. Nevertheless, several other major countries still are part of EU which controls many aspects of European political life.