A minimal custom exception definition:

public class CustomException : Exception // inherit from Exception rather than from ApplicationException
{
    public CustomException() { }
    public CustomException(string message) : base(message) { }
    public CustomException(string message, Exception innerException) : base(message, innerException) { }
}

A custom exception that overrides the Message property:

public class CustomException : Exception 
{
    // Override the Exception.Message property.
    public override string Message
    {
        get
        {
            StringBuilder sb = new StringBuilder();
            sb.Append("Time: " + DateTime.Now.ToString("f") + Environment.NewLine); // long date + short time
            sb.Append("Type: " + this.GetType().ToString() + Environment.NewLine);
            sb.Append("Message: " + base.Message + Environment.NewLine);
            if (this.InnerException != null) 
                sb.Append("Inner Message: " + this.InnerException.Message + Environment.NewLine);
            return sb.ToString();
        }
    }
 
    public CustomException() { }
    public CustomException(string message) : base(message) { }
    public CustomException(string message, Exception innerException) : base(message, innerException) { }
}

A method that iterates over all inner exceptions and returns their messages and types:

public string GetExceptionDesc(Exception exc)
{
    StringBuilder sb = new StringBuilder();
 
    sb.AppendLine("*** EXCEPTION ***");
    sb.AppendLine("DateTime: " + DateTime.Now.ToString());
    sb.AppendLine("Message: " + exc.Message);
    sb.AppendLine("Type: " + exc.GetType().ToString());
    sb.AppendLine("StackTrace: " + exc.StackTrace);
    AppendInnerExceptions(exc.InnerException, sb, 1);
 
    return sb.ToString();
}
 
private void AppendInnerExceptions(Exception exc, StringBuilder sb, int level)
{
    if (exc != null)
    {
        sb.AppendLine(String.Format("InnerException-{0} Message: {1}", level.ToString(), exc.Message));
        sb.AppendLine(String.Format("InnerException-{0} Type: {1}", level.ToString(), exc.GetType().Name));
 
        AppendInnerExceptions(exc.InnerException, sb, ++level);
    }
}

A custom exception that implements ISerializable:

// The SerializableAttribute ensures that the custom exception 
// can be serialized and works correctly across application domains 
// (for example, when a web service returns an exception).
[Serializable]
public class CustomException : Exception 
{
    // Custom properties for serialization.
    public int ExceptionNumber { get; private set; }
    public string MethodName { get; private set; }
 
    // A constructor accepting values for custom properties.
    public CustomException(string message, Exception innerException, int exceptionNumber, string methodName)
        : base(message, innerException)
    {
        this.ExceptionNumber = exceptionNumber;
        this.MethodName = methodName;
    }
 
    #region ISerializable Implementation
    protected CustomException(SerializationInfo info, StreamingContext context)
        : base(info, context)
    {
        // Get the custom property out of the serialization stream and set the object's property.
        ExceptionNumber = info.GetInt32("ExceptionNumber");
        MethodName = info.GetString("MethodName");
    }
 
    // The GetObjectData method is called  on serialization. 
    public override void GetObjectData(SerializationInfo info, StreamingContext context)
    {
        // Add the custom property into the serialization stream.
        info.AddValue("ExceptionNumber", ExceptionNumber);
        info.AddValue("MethodName", MethodName);
 
        // Call the base exception class to ensure proper serialization.
        base.GetObjectData(info, context);
    }
    #endregion
}

An exception builder is a helper method that creates and throws exceptions. A method that calls the exception builder is inlined by the compiler:

public class CustomException : Exception
{
    public CustomException(string message) : base(message) { }
}
 
// Enum values representing errors.
public enum ErrorCode
{
    NotInitialized,
    InvalidArgument,
    TimeOut
}
...
// An exception builder method that creates and throws CustomException.
private static void ThrowException(ErrorCode code)
{
    string message = "";
 
    switch (code)
    {
        case ErrorCode.NotInitialized:
            message = "Component is not initialized ...";
            break;
        case ErrorCode.InvalidArgument:
            message = "Invalid argument passed ...";
            break;
        case ErrorCode.TimeOut:
            message = "Time-out ocurred ...";
            break;
        default:
            message = "Generic exception.";
            break;
    }
 
    throw new CustomException(message);
}
...
// This method builds exceptions using the exception builder.
// As it does not use 'throw' to throw exceptions, it is inlined by the compiler.
public void DoSomething()
{
    // ...
    ThrowException(ErrorCode.NotInitialized);
    // ...
}

An example of implementing a SoapException wrapper:

using System;
using System.Text;
using System.Web.Services.Protocols;
using System.Xml;
...
public class SoapExceptionWrapper
{
    private long code;
    private string description;
    private string type;
 
    public long Code { get { return code; } }
    public string Description { get { return description; } }
    public string Type { get { return type; } }
 
    public SoapExceptionWrapper(SoapException exc)
    {
        if (exc.Detail != null && exc.Detail.InnerXml != "")
        {
            XmlDocument doc = new XmlDocument();
            doc.LoadXml(exc.Detail.InnerXml);
 
            if (doc.DocumentElement != null && doc.DocumentElement.Name == "error")
            {
                this.code =
                    Convert.ToInt64(doc.DocumentElement.SelectSingleNode("/error/code").InnerText, 16);
                this.description = doc.DocumentElement.SelectSingleNode("/error/description").InnerText;
                this.type = doc.DocumentElement.SelectSingleNode("/error/type").InnerText;
            }
            else
            {
                this.code = 0;
                this.description = "No error";
            }
        }
        else if (exc.GetBaseException() != null)
        {
            this.code = 0;
            this.description = exc.GetBaseException().Message;
            this.type = exc.GetBaseException().GetType().ToString();
        }
    }
 
    public override string ToString()
    {
        StringBuilder sb = new StringBuilder();
 
        sb.Append("SoapException Details:" + Environment.NewLine);
        sb.Append("    Code: " + this.code + Environment.NewLine);
        sb.Append("    Description: " + this.description + Environment.NewLine);
        sb.Append("    Type: " + this.type + Environment.NewLine);
 
        return sb.ToString();
    }
}

Exception types that are suitable to throw in custom code:

Exception types that should not be thrown in custom code:

• MSDN: Handling and Throwing Exceptions
• MSDN: Best Practices for Exceptions