There is a sample C# softphone in the CTIOS tookit in C:\Program Files\Cisco Systems\CTIOS Client\CTIOS Toolkit\dotNet CIL\Samples\CTI Toolkit Combo Desktop.NET

The CTIOS .NET CIL is not currently supported as a remoted component and there is no sample application using .NET Web forms. Currently the only supported architecture is a windows form based .NET CIIL application.

Other web based solutions which do not involve .NET and .ASP are conceivable by creating a java applet hosted in a browser or an activex control signed and hosted in a browser. Both of these require the CTIOS Cil to be installed on the local machine.

I have heard of an html based solution which uses the refresh and http post to update the state of the web page/softphone.

David is right on with his explanation.
We are working through a beta release of a web client that does not require any libraries and utilizes a piece of server side CTI/API and standard HTTP request.

Peace,
Michael Clendening
CCIE #6487 (ISP-Dial)