The answer, based on some research from Dave Hoffman is 360,000. This pales in comparison next to the 106,000,000 commenced in state court.

Now, I wonder how many of the cases that started in state court were removed to federal court?

This would be an excellent type of question to ask Harlan. To my knowledge, this would be next-to-impossible to find on Westlaw, and unless the FJC releases it in a report, it would remain a mystery.