I'm curious about how .NET will affect Python and Ruby applications. 
Will applications written in IronPython/IronRuby be so specific to the .NET environment, that they will essentially become platform specific? 
If they don't use any of the .NET features, then what is the advantage of IronPython/IronRuby over their non .NET counterparts?
Will applications written in IronPython/IronRuby be so specific to the .NET environment, that they will essentially become platform specific?

IronRuby currently ships with most of the core ruby standard library, and support for ruby gems.
This means that it will support pretty much any native ruby app that doesn't rely on C extensions.
The flipside is that it will be possible to write native ruby apps in IronRuby that don't rely on the CLR, and those will be portable to MRI. 
Whether or not people choose to create or use extensions for their apps using the CLR is the same question as to whether people create or use C extensions for MRI - one is no more portable than the other.
There is a side-question of "because it is so much easier to create IronRuby extensions in C# than it is to create CRuby extensions in C, will people create extensions where they should be sticking to native ruby code?", but that's entirely subjective.
On the whole though, I think anything that makes creating extensions easier is a big win.


If they don't use any of the .NET features, then what is the advantage of IronPython/IronRuby over their non .NET counterparts?


Performance: IronRuby is already faster for the most part than MRI 1.8, and isn't far off MRI 1.9, and things will only improve in future. I think python is similar in this respect.
Deployment: As people have mentioned, running a native ruby cross-platform rails app inside IIS is an attractive proposition to some windows-based developers, as it lets them better integrate with existing servers/management infrastructure/etc
Stability: While MRI 1.9 is much better than 1.8 was, I don't think anyone could disagree that CLR has a much better garbage collector and base runtime than C ruby does.
How will Python and Ruby applications be affected by .NET?