We find non-critical string backgrounds in five and eight dimensions, holographically related to four-dimensional conformal field theories with N = 0 and N = 1 supersymmetries. In the five-dimensional case we find an AdS 5 background metric for a string model related to non-supersymmetric, conformal QCD with large number of colors and flavors and discuss the conjectured existence of a conformal window from the point of view of our solution. In the eight-dimensional string theory, we build a family of solutions of the form AdS 5 ×S 3 withS 3 a squashed three-sphere. For a special value of the ratio N f /N c , the background can be interpreted as the supersymmetric near-horizon limit of a system of color and flavor branes on R 1,3 times a known four-dimensional generalization of the cigar. The N = 1 dual theory with fundamental matter should have an IR fixed point only for a fixed ratio N f /N c . General features of the string/gauge theory correspondence for theories with fundamental flavors are also addressed.