How many shallow water drilling oil spills have occurred?

The number is not known or at least not published. The total number is spills from oil oil platforms is known and accounts for a very small percentage of all oil dumped or leaked into our waters.

The number of spills is known:

The Gulf of Mexico (267 spills)
The northeastern U.S. (140 spills)
The Mediterranean Sea (127 spills)
The Persian Gulf (108 spills)
The North Sea (75 spills)
Japan (60 spills)
Baltic Sea (52 spills)
United Kingdom and English Channel (49 spills)
Malaysia and Singapore (39 spills)
The west coast of France and north and west coasts of Spain (33 spills)
Korea (32 spills)

The vast bulk are shallow spills and very few leak much oil. There are certainly exceptions but shallow oil drilling gives us far easier solutions to the situations then deep water does.

The vast bulk of oil spilled into our waters is from permanent fixtures and sites. Pipelines are one example.