Determining whether a link is slice is a difficult and subtle problem which arises naturally when studying four-dimensional aspects of link theory. Our primary purpose in this work is to find obstructions to slicing a particular family of links called generalized doubles. A generalized double is a particular type of satellite link and can be specified by a knot K and a Brunnian link L with distinguished component α. In this work, we give a general procedure for analyzing the relationship between the concordance invariants of a knot K and those of any associated generalized double. We apply this procedure to several examples of generalized doubles. Moreover, we consider a specific family of generalized doubles called iterated Bing doubles BD_n(K) and provide a new proof for the fact that if BD_n( K) is slice for some n, then K is algebraically slice. The principal tools that we use in this work are branched covers of S³ and the geometric operation on knots called cabling. Several results studying the algebraic concordance classes of cable knots are also included.