I couldn't get the most popular answer to this question (above by Dario) to work properly. The result was weird, choppy animation with weird artifacts.
Best solution I have found so far:
https://github.com/XamlAnimatedGif/WpfAnimatedGif
You can install it with NuGet
PM> Install-Package WpfAnimatedGif
and to use it, at a new namespace to the Window where you want to add the gif image and use it as below
<Window x:Class="MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:gif="http://wpfanimatedgif.codeplex.com" <!-- THIS NAMESPACE -->
Title="MainWindow" Height="350" Width="525">
<Grid>
<!-- EXAMPLE USAGE BELOW -->
<Image gif:ImageBehavior.AnimatedSource="Images/animated.gif" />
The package is really neat, you can set some attributes like below
<Image gif:ImageBehavior.RepeatBehavior="3x"
gif:ImageBehavior.AnimatedSource="Images/animated.gif" />
and you can use it in your code as well:
var image = new BitmapImage();
image.BeginInit();
image.UriSource = new Uri(fileName);
image.EndInit();
ImageBehavior.SetAnimatedSource(img, image);
EDIT: Silverlight support
As per josh2112's comment if you want to add animated GIF support to your Silverlight project then use github.com/XamlAnimatedGif/XamlAnimatedGif
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