The aim of this work is to develop codes suitable for iterative decoding using the sum-product algorithm. To this end, codes with sparse parity-check matrices, large girth and good minimum distance are sought. A sparse parity-check matrix is essential for workable decoding complexity, leading to so-called low-density parity-check (LDPC) codes. Large girth results in reduced dependence in the message passing and so to more efficient iterative decoding, while large minimum distance improves the error floor performance of the code. Further, regular codes, that is codes with parity-check matrix with fixed row and column weights, can simplify the implementation of LDPC codes. We consider in this paper regular LDPC codes, derived from partial geometries, which have girth at least 6 and sparse parity-check matrices. Partial geometries are a large class of combinatorial structures whose incidence matrices include several of the previously proposed algebraic constructions for LDPC codes as special cases. These include Steiner triple systems, Kirkman triple systems, oval designs, generalized quadrangles, and some of the finite geometries of Lin and co-workers. We derive minimum distance bounds for codes from partial geometries, and present constructions and performance results for classes of partial geometries, namely transversal designs and the proper partial geometries, which have not previously been proposed for iterative decoding.