Tumbling oil prices are starting to frighten energy companies around the globe, especially drillers in North America, where crude is expensive to pump.

Global oil prices have fallen about 8% in the past four weeks. The European oil benchmark closed Thursday at $90.05 a barrel, its lowest point in 29 months. The price of a barrel in the U.S. closed at $85.77, its lowest since December 2012.

Weakening...