It's going to vary hugely from country to country.
Some countries require flight plans for flights into controlled airspace, and most of their airports are covered in controlled airspace. Therefore most flights will require plans (eg Ireland, Spain, Netherlands).
Others done, and very few flights will have plans (eg UK & USA).
Then what you call a plan will also affect the numbers.
The UK technically requires a flight plan to enter controlled airpace, but say that an "abbreviated flight plan" is sufficient. What is an abbreviated flight plan? Well, it's just a radio call. So technically it's a flight plan, but in reality most pilots "filing" that plan don't realise it's an abbreviated flight plan.
So the answer depends grately on where you're talking about and what you are defining as a plan.