C#: XmlTextWriter.WriteElementString fails on empty strings?

It doesn't fail <Tag/> is just a shortcut for <Tag></Tag>

Your output is correct. An element with no content should be written as <tag/>.

You can force the use of the full tag by calling WriteFullEndElement()

writer.WriteStartElement("Email");
writer.WriteString(inputEmail);
writer.WriteFullEndElement();

That will output <Email></Email> when inputEmail is empty.

If you want to do that more than once, you could create an extension method:

public static void WriteFullElementString(this XmlTextWriter writer,
                                          string localName, 
                                          string value)
{
    writer.WriteStartElement(localName);
    writer.WriteString(value);
    writer.WriteFullEndElement();
}

Then your code would become:

writer.WriteStartElement("User");
writer.WriteFullElementString("Username", inputUserName);
writer.WriteFullElementString("Email", inputEmail);
writer.WriteEndElement();

Your code should be:

using (XmlWriter writer = XmlWriter.Create("filename.xml"))
{
    writer.WriteStartElement("User");
    writer.WriteElementString("Username", inputUserName);
    writer.WriteElementString("Email", inputEmail);
    writer.WriteEndElement();
}

This avoids resource leaks in case of exceptions, and uses the proper way to create an XmlReader (since .NET 2.0).