I recently had this same problem. Unfortunately, NotifyIcon is only a Windows.Forms control at the moment, if you want to use it you are going to have to include that part of the framework. I guess that depends how much of a WPF purist you are.
If you want a quick and easy way of getting started check out this WPF NotifyIcon control on the Code Project which does not rely on the WinForms NotifyIcon at all. A more recent version seems to be available on the author's website and as a NuGet package. This seems like the best and cleanest way to me so far.
- Rich ToolTips rather than text
- WPF context menus and popups
- Command support and routed events
- Flexible data binding
- Rich balloon messages rather than the default messages provides by the OS
Check it out. It comes with an amazing sample app too, very easy to use, and you can have great looking Windows Live Messenger style WPF popups, tooltips, and context menus. Perfect for displaying an RSS feed, I am using it for a similar purpose.