Not only are anchovies paleo-friendly, they are among the most nutritious animals you can find. Because anchovies are eaten whole, you get the benefit of all of the nutrients that are packed into the bones and organs, as well as the flesh of the fish.
Anchovies are high in omega-3, a polyunsaturated fat which is anti-inflammatory and extremely beneficial for mental and cardiovascular health. Anchovies make an excellent addition to Paleo salad and as seasoning in homemade pasta sauce, or even salad dressing. Mark Sisson has a couple reasons why you should include anchovies as part of your diet
here and here.