The permanent and dynamic (transient) stress changes inferred to trigger earthquakes are usually orders of magnitude smaller than the stresses relaxed by the earthquakes themselves, implying that triggering occurs on critically stressed faults. Triggered seismicity rate increases may therefore be most likely to occur in areas where loading rates are highest and elevated pore pressures, perhaps facilitated by high-temperature fluids, reduce frictional stresses and promote failure. Here we show that the 2002 magnitude M = 7.9 Denali, Alaska, earthquake triggered widespread seismicity rate increases throughout British Columbia and into the western United States. Dynamic triggering by seismic waves should be enhanced in directions where rupture directivity focuses radiated energy, and we verify this using seismic and new high-sample GPS recordings of the Denali mainshock. These observations are comparable in scale only to the triggering caused by the 1992 M = 7.4 Landers, California, earthquake, and demonstrate that Landers triggering did not reflect some peculiarity of the region or the earthquake. However, the rate increases triggered by the Denali earthquake occurred in areas not obviously tectonically active, implying that even in areas of low ambient stressing rates, faults may still be critically stressed and that dynamic triggering may be ubiquitous and unpredictable.