Which programming languge has the most mature speech recognition api?
Probably doesn't matter - the recognition library will likely be written in C and so can be called from almost anything.
I don't think I'd call any speech recognition API "mature", but but I prefer the Managed Code Speech API, which comes free with .NET >= 3. So that means you can use any .NET language you like: C#, VB, C++.... even IronRuby
The Microsoft Speech API is a fairly mature speech API. It's pretty neat because as long as your end-users are on a supported platform, they can get the benefits from the Speech API. And I'm pretty sure it's freely available.
It's available in managed .NET code as the Managed Code Speech API: http://en.wikipedia.org/wiki/Microsoft_Speech_API#Managed_code_Speech_API
It's available in C/C++ (or really any language that can make COM calls) as Speech API 5: http://en.wikipedia.org/wiki/Microsoft_Speech_API#SAPI_5_API_family
The MSDN link to the speech API: http://msdn.microsoft.com/en-us/library/ms723627%28VS.85%29.aspx