The worm-like chain model has often been employed to describe the average conformation of long, intrinsically straight polymer molecules, including DNA. The present study extends the applicability of the worm-like chain model to polymers containing bends or sections of different flexibility. Several cases have been explicitly considered: (i) polymers with a single bend; (ii) polymers with multiple coplanar bends; (iii) polymers with two non-coplanar bends; and (iv) polymers comprised of sections with different persistence lengths. Expressions describing the average conformation of such polymers in terms of the mean-square end-to-end distance have been derived for each case. For cases (i) and (iv), expressions for the projection of the end-to-end vector onto the initial orientation of the chain are presented. The expressions derived here have been used to investigate DNA molecules with sequence-induced bending (A-tracts). Mean-square end-to-end distance values determined from a large number of A-tract containing DNA molecules visualized by scanning force microscopy resulted in an average bend angle of 13.5 degrees per A-tract. A similar study was performed to characterize the flexibility of double-strandedDNA molecules containing a single-stranded region. Analysis of their mean-square end-to-end distance yielded a persistence length of 1.3 nm for single-stranded DNA.