I know I can use SOAPExtension to read request and response SOAP messages on
the server side for a Web Method. Is there a way to do the same thing on the
client side when you make a Web Service call? I would like to see what is
going out and what is coming in. Thanks for your help.

This is the same:

this example was taken from Remoting WebService (Amit Kalani):

using System;
using System.IO;
using System.Xml;
using System.Xml.Xsl;
using System.Web.Services;
using System.Web.Services.Protocols;

namespace BugTrackerClient
{
/// <summary>
/// Summary description for SoapDisplayExtension.
/// </summary>
public class SoapDisplayExtension : SoapExtension
{
public SoapDisplayExtension()
{
//
// TODO: Add constructor logic here
//
}

// Variables to hold the original stream
// and the stream that we return
private Stream originalStream;
private Stream internalStream;

// Version called if configured with a config file
public override object GetInitializer(
System.Type serviceType)
{
// Not used in this example, but it//s
// declared abstract in the base class
return null;
}

// Called the first time the Web service is used
// Version called if configured with an attribute
public override object GetInitializer(
LogicalMethodInfo methodInfo,
SoapExtensionAttribute attribute)
{
// Not used in this example, but it//s
// declared abstract in the base class
return null;
}

// Called each time the Web service is used
// And gets passed the data from
// GetInitializer() method
public override void Initialize(
object initializer)
{
// Not used in this example, but it//s
// declared abstract in the base class
}

// The ChainStream() method gives us a chance
// to grab the SOAP messages as they go by
public override System.IO.Stream ChainStream(
System.IO.Stream stream)
{
// Save the original stream
originalStream = stream;
// Create and return our own in its place
internalStream = new MemoryStream();
return internalStream;
}

// The ProcessMessage() method is where we do our work
public override void ProcessMessage(
System.Web.Services.Protocols.SoapMessage message)
{
// Determine the stage and take appropriate action
switch(message.Stage)
{
case SoapMessageStage.BeforeSerialize:
// About to prepare a SOAP Response
break;

case SoapMessageStage.AfterSerialize:
// SOAP response is all prepared
internalStream.Position = 0;
// Get a Transform ready
XslTransform xslt = new XslTransform();
xslt.Load(@"..\..\Identity.xslt");
// Load the raw XML into an XML document
XmlDocument xd = new XmlDocument();
xd.Load(internalStream);
// Use the transform to pretty print it
MemoryStream ms = new MemoryStream();
xslt.Transform(xd, null, ms);
// And drop the results
// to a TextBox control
ms.Position = 0;
StreamReader sr = new StreamReader(ms);
DisplayMessage f = new DisplayMessage();
f.txtMessage.Text = sr.ReadToEnd();
f.Show();
// Copy the passed message
// to the other stream
internalStream.Position = 0;
CopyStream(
internalStream, originalStream);
internalStream.Position = 0;
break;

case SoapMessageStage.BeforeDeserialize:
// About to handle a SOAP request
// Copy the passed message
// to the other stream
CopyStream(
originalStream, internalStream);
internalStream.Position = 0;
// Get a Transform ready
XslTransform xslt1 = new XslTransform();
xslt1.Load(@"..\..\Identity.xslt");
// Load the raw XML into an XML document
XmlDocument xd1 = new XmlDocument();
xd1.Load(internalStream);
// Use the transform to pretty print it
MemoryStream ms1 = new MemoryStream();
xslt1.Transform(xd1, null, ms1);
// And drop the results
// to a TextBox control
ms1.Position = 0;
StreamReader sr1 = new StreamReader(ms1);
DisplayMessage f1 = new DisplayMessage();
f1.txtMessage.Text = sr1.ReadToEnd();
f1.Show();
internalStream.Position = 0;
break;

case SoapMessageStage.AfterDeserialize:
// SOAP request has been deserialized
break;
}
}

// Helper function to copy one stream to another
private void CopyStream(Stream fromStream,
Stream toStream)
{
try
{
StreamReader sr =
new StreamReader(fromStream);
StreamWriter sw =
new StreamWriter(toStream);
sw.WriteLine(sr.ReadToEnd());
sw.Flush();
}
catch (Exception ex)
{
// Log the exception
}
}
}
}