Here is every method that raises happiness in Pokemon. Some of these aren't possible in every generation, so check which ones are available to you.
In general, keeping a Pokémon in your party, raising its level, using items on it, and getting it groomed will increase a Pokémon's friendship. Other than that, here are some more specific ways you can increase friendship.
- Catch a Pokemon in a Friend Ball (instant 200 Friendship - See Friend Ball Locations)
- Catch a Pokemon in a Luxury Ball (Every increase in friendship will be boosted by 1 point - See Luxury Ball locations)
- Pokemon hatched from an egg start with 120 Friendship
- From Crystal onwards, (except in Gen IV) any action that raises friendship is boosted if it happens in the met location of your Pokemon, (i.e, where it was caught). This boost is x2 in Crystal and a boost of 1 point in all other games where it applies.
- Equipping your Pokemon with a Soothe Bell causes increases in friendship to be boosted by 50%.
- Specific berries increase friendship drastically. Pomeg, Kelpsy, Qualot, Hondew, Grepa, and Tamato berries all raise friendship while decreasing HP, Attack, Defense, Sp.Atk, Sp.Def, and Speed EVs respectively.
- Leveling up a Pokemon or giving it a vitamin will increase its friendship by a maximum of 5 points.
- Using a feather on a Pokemon increases its friendship by a maximum of 3 points.
Other more obscure methods include challenging a Gym Leader or the Elite Four, using a TM/HM pre-Gen VI, using battle items, or walking certain amounts of steps.
Here are some game-specific ways to increase friendship:
- Purifying a Pokemon in Colosseum/XD increases it's friendship by 70 points.
- Winning a contest in Gen IV increases friendship slightly.
- Getting a haircut at the Beauty Salon on Join Avenue in B2W2 causes vast increases in friendship.
- Using the Soothing Bag in Super Training increases friendship by 20 points.
- Getting a drink made at the Juice Shoppe in Lumiose City in XY variably increases friendship.
- Putting your Pokemon in Isle Avue on Poke Pelago causes a 5-point increase in friendship.
- Throwing money in the fountain in Cerulean City in LGPE causes a party-wide increase of 20 points.
- Playing with your Pokemon in Pokemon Camp slightly increases happiness.
- Feeding a Pokemon a Poffin slightly increases happiness in BDSP.
The only ways to decrease happiness are by fainting or giving your Pokemon herbal medicine.
And I think that's it! It's important to note that friendship-increasing actions often yield fewer gains as friendship increases. You can see more about that here.
I hope I could help! Please let me know if I have any major misses.