3 Machamps: I shouldn't need to explain this. I often use them at half HP, which is why I need 3 of them.
There is a reason why I put the slightly lower IV Machamp first. That Machamp is A/D/S 15/12/15, so there is practically no difference in battle.
If I'm fighting a GRB-defended mon in the first slot repeatedly, I will move a mon that is super effective to the first mon to the first slot in the party. When I change it back to Machamp, I keep selecting the wrong Machamp if I use one of the 100% ones. I don't have this problem with the 93% one.
Rayquaza: For Dragonites/Salamence (and the occasional Machamp/Hariyama) in gyms. Lower level dragons may get knocked out with a single Outrage.
Sometimes replaced with a L30 DB/DC Dragonite.
Zapdos: For Vaporeon/Gyarados/Milotic. I don't usually use Raikou as it's not my team's mascot.
Replaced with Raikou if I'm fighting a GRB-defended water type with ice moves.
Last slot: Depends. Sometimes another Machamp, sometimes another Dragonite, sometimes a Lugia. If I'm farming gym badge points at a gym already under heavy attack (with 3+ attackers), I will put the Lugia in the first slot and move the first Machamp here (to continue to rack up battles won).