PokéBase - Pokémon Q&A
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I love the data sheets this site has with all moves per generation and their corresponding details, but I want a comprehensive spreadsheet including which Pokémon can learn which moves.

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For everything up to US/UM, PokeAPI has all of this covered. You can find all their raw data in CSV in their GitHub repo. Pokemon learnsets specifically can be seen here (access via GitHub to download).

You can open CSV in Excel if you want, but care that these are very large files and they're meant for use in databases (and of course, the API), not for you to read in a spreadsheet. The data is presented using ID numbers, which you could link to the "names" of each item in Excel by downloading all the other sheets that link IDs to names, or write a program that does it. Might take a while though.

If you want data for LGP/E, SW/SH or BD/SP then things get a bit tricky, because PokeAPI developers are resistant to any source that isn't direct from the games themselves, and their original source Veekun hasn't added new data for those games. There is a fork where they are apparently scraping data from Bulbapedia, but it's not up to date either. You can keep track of it here.

I had a look for alternative sources for each "missing" game, and found the following:

You might find some better stuff if you trawl GitHub for a while. Pokemon Showdown has some data but it's entirely filtered by generation, not by game, and is not in a spreadsheet format (which you'll have to get used to). It seems to be up-to-date, though?

It's possible that Pokemondb.net itself has the "most complete" and most granular learnset data (though it is known to miss some event moves). Pokemaster (who runs the site) has shown interest in publicly distributing the data, but he hasn't made any learnset data public. Not sure how Serebii sources their data but it isn't public either.

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Pokemon Showdown also has their list in JSON format: https://raw.githubusercontent.com/smogon/pokemon-showdown/master/data/learnsets.ts Their syntax is one that takes some getting used to, though: moves could be tagged with designations like "3M" (generation 3 TM move), "4L15" (generation 4, level-up move at level 15 or higher), "6E" (generation 6 egg move), or "7V" (a move that can be obtained from Virtual Console version of the Game Boy games, from which it can go to Bank and only rejoin other Pokemon in a game from 7 or later).
This is such good information!  Very detailed and thorough!  Thank you so much for all your help here!!