Tools
Calculators based on the games' code: the FireRed decompilation for Generation 3, the Pokémon Showdown simulator for recent games.
Damage calculator
Gen 3 (RSE / FRLG, exact) · Modern (Showdown, gen 6-9)
Catch calculator
Gen 3 (RSE / FRLG, exact)
Spinda Maker · ShinyGen soon
Spinda Maker, ShinyGen: free RNG tools.