The U.S. oil industry--apparently spurred by higher, unregulated oil prices--drilled a record 78,884 oil and gas wells last year, a 25.8 percent increase over 1980.

The Petroleum Information Corp., which gathers information on drilling activity across the nation, said the industry completed more oil wells than ever before, 39,101. The industry also completed 16,095 gas wells, 7.3 percent more than in 1980.

Most of the wells that were drilled were for development--that is, in fields already known to have oil and gas deposits. But the company said there was a sharp increase in wildcat wells sunk for entirely exploratory purposes. The oil and gas industry drilled 9,331 wells in search of new oil and gas fields last year, an increase of 25.7 percent over 1980.

More than 7,600 of the new wildcat wells turned up neither oil nor gas--or at least not enough of either to make production commercially possible. Nevertheless, 18.4 percent of the exploratory wells that were drilled were successful, according to Petroleum Information Corp. That success rate is lower than in either 1980 or 1979, but is above the 17.9 percent average since 1974.

By contrast, development wells found oil and gas 80 percent of the time.