Anchovies and dishes with Anchovies in them are extremely salty. Therefore you want to pair them up with chilled white wines that are high in acidity, and lightly oaked.
A Sauvignon Blanc from New Zealand would work beautifully, as it is pungent on the nose like anchovies are, but the flavours are tangy and crisp making it quite refreshing.
Other white wines that work well are, Orvieto, Sancerre, Pinot Grigio, Albarino, or a Pinot Blanc from Alsace.
Sweet wines with a high acidity are another option as they help balance the salt of the Anchovies and a higher acidity helps the wine stand up to the intensiveness of the anchovies. A German Riesling would be exceptional in this case, as would and off-dry or semi-sweet Riesling.