Stand Up And Cheer
Ed Sim has a really good post on what to do when your competitor is acquired. If you run a company and are facing this issue, you really should go read Ed's post.
But I have some shorter and simpler advice.
Stand Up and Cheer. Loudly.
Because the vicious competitor you've been facing off with in the market will be no more. They'll be subsumed into some corporate culture. Their driven entrepreneurial leadership will be counting the days until they are free to leave to start another company and thinking about how to intelligently invest the millions they just made. And the best employees will have their resumes on the street, possibly for you to hire. And their customers will be looking around to see if they should be moving on too.
Trust me on this one. I've seen this movie about fifty times. It almost always ends happily.