From Wikipedia:
"A pandemic is an epidemic occurring on a scale that crosses international boundaries, usually affecting people on a worldwide scale."
"An epidemic is the rapid spread of disease to a large number of patients among a given population within an area in a short period of time."
Simply existing in many different countries isn't enough; there has to be large-scale spread in those countries.
In addition, the disease must have a noticeable impact on normal human life. It will not count if a new pathogen emerges and spreads virulently across the globe, but is completely harmless and there are no significant efforts to prevent its spread.
If anyone feels this definition is too vague for you to be comfortable betting, tell me how I could effectively reduce the ambiguity and I'll update this description as necessary.
I think this is probably the most reasonable list:
https://en.wikipedia.org/wiki/Third_plague_pandemic
https://en.wikipedia.org/wiki/Spanish_flu
https://en.wikipedia.org/wiki/Encephalitis_lethargica#Pandemic_of_1915%E2%80%931926
https://en.wikipedia.org/wiki/1957%E2%80%931958_influenza_pandemic
https://en.wikipedia.org/wiki/Hong_Kong_flu
https://en.wikipedia.org/wiki/1977_Russian_flu
https://en.wikipedia.org/wiki/Epidemiology_of_HIV/AIDS
https://en.wikipedia.org/wiki/2009_swine_flu_pandemic
https://en.wikipedia.org/wiki/COVID-19_pandemic
Unsure on some of them, as it's unclear whether they actually had a significant effect on other countries, or just had a few cases there and this got them classified as "worldwide". I'm particularly confused at the lack of information available online about the 1977 Russian flu. Seems like something that caused 700,000 deaths should have a lot more writing about it.
Basically, if it doesn't affect the day-to-day life of normal people on different continents, I don't want to count it.