<p>What are some of the best or most popular rule engines?  I haven't settled on a programming language, so tell me the rule engine and what programming languages it supports.</p>

I have a bit of experience with both Haley Expert Rules and Haley Office Rules. Both nice systems, but I'd need to know a bit more abut what you want to use them for to answer definitively (See
http://www.haley.com
)
They both support C# and Java (and I think also a web service api).
The difference between the two is mostly around how much natural language modelling you want to get into. Office rules lets business users write rules in an Office document, and is mostly focused around legislative requirements modelling. Expert rules can be a bit more flexible in definition how it handles natural language, but requires more work defining language structures up front.
Hope some of that helps.