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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, several Pokemon have had their base stat changes modified in the past. The first instance of this, while not explicitly a change to the actual base stat values, occurred in Generation 2 with the split of the Special stat from Generation 1. The Special stat was replaced by Special Attack and Special Defence with the release of Gold and Silver, so Generation 1 Pokemon effectively received brand new base stats as a result. Some Pokemon retained their old Special base stat value for both Special Attack and Special Defence, whilst others retained their Special stat value for only one or the other.

It is interesting to note, however, that IVs and EVs were unchanged by these changes in Generation 2, presumably to avoid complications when transferring Generation 1 Pokemon to Generation 2. So in Generation 2, all Pokemon's Special Attack and Special Defence IVs and EVs were identical, but their base stats were not. In Generation 3, the stats were made fully separate and have remained unchanged since.

Later, going from Generation 5 into Generation 6, a variety of Pokemon experienced direct base stat changes, all of whom received 10 extra base stat points on one or two of their stats. The list of these Pokemon, according to Serebii, can be found below and at the address linked here.

  • 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.

Again, some Pokemon received base stat modifications going from Generation 6 to Generation 7. These were leaked prior to Sun and Moon's release by Kaphotics, and can be seen here alongside changes to some Pokemon's abilities.

To verify, affected Pokemon transferred from Generation 5 to Generation 6 (and to Generation 7) will experience a change in stat points in accordance to these changes, as the Pokemon's stats are recalculated when they are moved to the new game.

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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