The U.S. and the Organization of the Petroleum Exporting Countries have flooded the world with crude oil, sending prices tumbling. But the abundance has overshadowed declining production in areas—from Colombia to Norway to northern China—that experts consider vital to long-term supply growth.

Confronted with the plunge in prices, companies in these regions are delaying and canceling projects. Across the world, just six major oil projects received the green light in 2014, compared with an average of more than 20 a year from...