This paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), an integrated algorithmic framework for SAT that unifies several previously proposed search-pruning techniques and facilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search spare. In addition, by "recording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks, including many from the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances.