Question: Has anyone here had any experience with running OpenBD or Railo in production? We have some legacy CF6.1 apps that need to be hosted somewhere and I'm wondering if OpenBD or Railo is stable enough for production use, won't require a great deal effort to migrate to, etc.

Answer: 
Absolutely! Both are enterprise class solutions and shouldn't pose too many problems. As rip747 mentions there are copies you can download to quickly test your applications compatibility.

As for performance it's generally believed that Railo is the fastest of the three engines while BlueDragon is the slowest. Although it's not currently in production I'm developing an application against Railo 3.0 and intend to deploy to Railo 3.1 once it's released.
Rob, mind if I try to solve your problem by providing a different solution than your question asks?

In that you mention an interest in hosting, just keep in mind that if you mean shared hosting, then you don't need to worry about the cost of the CFML engine. That will be born by the hosting provider, and amortized over the folks on the server. As such, you will find many low- (and even no-) cost CF hosting providers running on Adobe CF (and you'll find a range of them running different versions to suit one's taste, from CF 6, 7, 8, or 9, as I write today.)

There are various lists of CF hosting providers. I offer one (and also provide pointers to still other lists) at a category of my CF411 site: <http://www.cf411.com/#cfhost>