What is the latest recommended method for having multiple client desktop application pass information to a server application located across the internet?

I am using c# and Vis studio 2008, and not sure if SOAP is appropriate or maybe SOAP has been superseded by WCF.
Or maybe there are other methods that are more suitable.

I would look at WCF more closely it is based on SOAP and may be what you are looking for by the sounds of it.

See:
Microsoft What is WCF

WCF is the "latest and greatest" but tou can also take a look at remoting. I am in the middle of a project with similar requirements and WCF scared me back in to remoting. I know microsoft is promoting WCF but I just haven't been able to find enough resources and support with the designer for all of the decorating WCF requires.

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