How many Pokémon appeared in the original Generation 1 games (Red and Blue)?

How to get close to this number

This is the number the franchise anchored itself on, and almost everyone who was a child in the late nineties can recall it exactly. It is worth noticing that the recall is unusually precise for a trivia figure — the original set was small enough to memorise completely, which is exactly why it stuck.

The Mew detail is the part that made the number famous. The final entry was not obtainable in normal play and required a special event, which turned a complete Pokédex into something most players could never finish. A deliberately unreachable last item is a powerful design device, and it generated years of playground rumour about how to get it.

The contrast with the modern total is the estimation lesson from this site's companion question: the franchise has since passed a thousand species. Anyone anchoring on this figure and adjusting upward will still land far short, because the anchor is so strongly held. Knowing the original is useful; knowing that it is an anchor is more useful.