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Title should be self explanatory. If you had, say an Arceus, in Generation four and had 100 in each base stat (I know it didn't, I'm using it as an example) and then its base stats got increased by 20 to 120 in generation five. I'm basically looking for any Pokemon that has done that. Or decreased, doesn't have to be increased only.

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Yes. The first instance of this, while not a direct change to the actual base stat values, occurred in Gen 2 with the split of the Special stat from Gen 1. The Special stat was replaced by Special Attack and Special Defence, so Gen 1 Pokemon effectively received brand new base stats. Each Pokemon's old Special stat lives on through its SpA stat or its SpD stat.

Between Gen 5 and Gen 6, a variety of Pokemon experienced direct base stat changes. The list of these Pokemon, according to Serebii, can be found below:

  • Butterfree's base Special Attack was increased from 80 to 90.
  • Beedrill's base Attack was increased from 80 to 90.
  • Pidgeot's base Speed was increased from 91 to 101.
  • Pikachu's base Defence and Special Defence was increased from 30 to 40 and 40 to 50 respectively.
  • Raichu's base Speed was increased from 100 to 110.
  • Nidoqueen's base Attack was increased from 82 to 92.
  • Nidoking's base Attack was increased from 92 to 102.
  • Clefable's base Special Attack was increased from 85 to 95.
  • Wigglytuff's base Special Attack was increased from 75 to 85.
  • Vileplume's base Special Attack was increased from 100 to 110.
  • Poliwrath's base Attack was increased from 85 to 95.
  • Alakazam's base Special Defence was increased from 85 to 95.
  • Victreebel's base Special Defence was increased from 60 to 70.
  • Golem's base Attack was increased from 110 to 120.
  • Ampharos' base Defence was increased from 75 to 85.
  • Bellossom's base Defence was increased from 85 to 95.
  • Azumarill's base Special Attack was increased from 50 to 60.
  • Jumpluff's base Special Defence was increased from 85 to 95.
  • Beautifly's base Special Attack was increased from 90 to 100.
  • Exploud's base Special Defence was increased from 63 to 73.
  • Staraptor's base Special Defence was increased from 50 to 60.
  • Roserade's base Defence was increased from 55 to 65.
  • Stoutland's base Attack was increased from 100 to 110.
  • Unfezant's base Attack was increased from 105 to 115.
  • Gigalith's base Special Defence was increased from 70 to 80.
  • Seismitoad's base Attack was increased from 85 to 95.
  • Leavanny's base Special Defence was increased from 70 to 80.
  • Scolipede's base Attack was increased from 90 to 100.
  • Krookodile's base Defence was increased from 70 to 80.

Once again, between Gen 6 and Gen 7, base stat changes occurred. They are listed as follows (credit Kaphotics):

  • Arbok's base Attack was increased from 85 to 95.
  • Dugtrio's base Attack was increased from 80 to 100.
  • Farfetch'd's base Attack was increased from 65 to 90.
  • Dodrio's base Speed was increased from 100 to 110.
  • Electrode's base Speed was increased from 140 to 150.
  • Exeggutor's base Special Defence was increased from 65 to 75.
  • Noctowl's base Special Attack was increased from 76 to 86.
  • Ariados's base Special Defence was increased from 60 to 70.
  • Qwilfish's base Defence was increased from 75 to 85.
  • Magcargo's base HP and Special Attack was increased from 50 to 60 and 80 to 90 respectively.
  • Corsola's base HP, Defence and Special Defence was increased from 55 to 65, 85 to 95 and 85 to 95 respectively.
  • Mantine's base HP was increased from 65 to 85.
  • Swellow's base Special Attack was increased from 50 to 75.
  • Pelipper's base Special Attack was increased from 85 to 95.
  • Masquerain's base Special Attack and Speed was increased from 80 to 100 and 60 to 80 respectively.
  • Delcatty's base Speed was increased from 70 to 90.
  • Volbeat's base Defence and Special Defence was increased from 55 to 75 and 75 to 85 respectively.
  • Lunatone's base HP was increased from 70 to 90.
  • Solrock's base HP was increased from 70 to 90.
  • Chimecho's base HP, Defence and Special Defence was increased from 65 to 75, 70 to 80 and 80 to 90 respectively.
  • Woobat's base HP was increased from 55 to 65.
  • Crustle's base Attack was increased from 95 to 105.
  • Beartic's base Attack was increased from 110 to 130.
  • Cryogonal's base HP and Defence was increased from 70 to 80 and 30 to 50 respectively.
  • Mega Alakazam's base Special Defence was increased from 95 to 105.

Between Gen 7 and Gen 8, Aegislash's base Defence and Special Defence were both reduced from 150 to 140.

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Thanks. I had no idea if there were any. Are there base stat changes shown on the DB pokedex pages though for that list?
The DB Pokedex pages are up to date with the current base stats, but no, currently there is no list of base stat changes on the DB or any notice of the changes on any individual Pokemon's page. I might actually edit this answer to include the list, so that it's here too.
Well I feel stupid