At the time of writing, Bulbapedia lists 61 distinct events for Mew. Due to the length of the list it would be easier to view it here. Thus, if you were able to obtain just one Mew from each distinct distribution, anywhere, anytime, on just one of the participating games, you would have 61 of them.
Note that some of these events share the same Mew set but are considered distinct due to different distribution locations or time periods (e.g., there were 5 "Fall 2010 Mew" events for 5 different languages). If you want to count events with the same name as the same event, there are 45 unique events. The only caveat with this approach is that one of the five "Game Freak Mew" distributions was for Gen 1 Virtual Console, whereas the others were for Gen 6, so that one is technically different from the other four due to the limitations of Gen 1.
Conversely, some events contain multiple different Mew sets but only one could be obtained per player (e.g., the "My very own Mew" event for Scarlet and Violet could have different Tera types).
Additionally, 3 of the listed events are Poke Ball Plus distributions; one for LGPE in Mainland China that spans from September 26, 2024 to May 15, 2026, one for LGPE everywhere else with no end date, and one for Sword/Shield with no end date.
I am not counting the possibility of obtaining more than one Mew from the same event, although it is possible, whether it's by using another copy of the game or visiting the same in-person event multiple times. So for instance, for the German Aura Mew event where you could get Mew at McDonald's, I am not counting the ability to go to more than one McDonald's.
