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 x tilde{S}^3 with tilde{S}^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.
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