Any 2 pokemon that you always use together?

Often use Mewtwo and Lugia in a pair. Using them means either:
#1: Countering something that is weak to Psychic and/or Flying
#2: Battling against something that is Psychic-type
#3: I need generalist power because I am lacking in high-DPS specialized counters.

They make a great pair, especially since Mewtwo is relatively glassy and Lugia more than makes up for that. Lugia is a great choice for the last slot of a team because it is easy to dodge with, super tanky, has decent damage, and can quickly get off a Charged Move which is valuable for the "overkill" damage bonus in raids.

I guess my two Pokémon just depend on the raid I’m doing. It mostly consists of using Espeon and Alakazam together for fighting/poison and using Gyarados and Vape for anything weak to water. I lack almost all of the legendaries besides Ray and Groudon and the ones “handed” to me.

Machamp and Dragonite. The dragonite finishes what the machamp starts if the gym is at full strength (although I go for 8 hour gyms but people will feed them). In raids I normally use teams for a specific boss. My Shiftry and Houndoom would be for psychic type raids like Latios.
My 100% Xatu pair are always part of the Machamp team. Soloed a boosted Machamp that had CC yesterday.

Well, the trivial answer of Machamp and Machamp, Rauquaza and Rayquaza, etc.

Also, Espeon and Psychic Mewtwo, Flying Rayquaza and Sky attack Lugia, Rayquaza and Dragonite (for most legendary dragon raids).