We present a new quasi-model-independent strategy (''Sleuth'') for searching for physics beyond the standard model. We define final states to be studied, and construct a rule that identifies a set of relevant variables for any particular final state. A novel algorithm searches for regions of excess in those variables and quantifies the significance of any detected excess. This strategy is applied to search for new high p{_}T physics in approximately 100 pb{sup -1} of proton-anti-proton collisions at sqrt(s) = 1.8 TeV collected by the D0 experiment during 1992-1996 at the Fermilab Tevatron. We systematically analyze many exclusive final states, and demonstrate sensitivity to a variety of models predicting new phenomena at the electroweak scale. No evidence of new high p{_}T physics is observed.