Showing ClickOnce deployment version on WPF application

What error do you get? There's no difference in the ClickOnce API's between Windows Forms and WPF. It is not dependent upon any UI framework.

Did you remember to add a reference to System.Deployment.dll?

Try this:

public static Version GetPublishedVersion()
{
    XmlDocument xmlDoc = new XmlDocument();
    Assembly asmCurrent = System.Reflection.Assembly.GetExecutingAssembly();
    string executePath = new Uri(asmCurrent.GetName().CodeBase).LocalPath;

    xmlDoc.Load(executePath + ".manifest");
    string retval = string.Empty;
    if (xmlDoc.HasChildNodes)
    {
        retval = xmlDoc.ChildNodes[1].ChildNodes[0].Attributes.GetNamedItem("version").Value.ToString();
    }
    return new Version(retval);
}

using System;
using System.Deployment.Application;

namespace Utils
{
    public class ClickOnce
    {
        public static Version GetPublishedVersion()
        {
            return ApplicationDeployment.IsNetworkDeployed 
                ? ApplicationDeployment.CurrentDeployment.CurrentVersion 
                : System.Reflection.Assembly.GetExecutingAssembly().GetName().Version;
        }
    }
}

If you get an error about System.Deployment.Application, then Solution > Project > References > Add Reference > Assemblies > Framework > System.Deployment.

Do not parse the assembly XML for this information; you're relying on undocumented behaviour which simply happens to work 'for now'.