Find Majors and Ultras for each species

I have found that Devil's Lair is the best place to farm Fallen Ultras. In the first area with the Fallen Walker event, there is a dropship that will periodically drop off 4 Fallen Vandals, one of them being a Major.

Shows up in this area, behind the building:

For the Hive, I like doing the Sword of Crota mission. There is 5 Ultras in there, including the Swarm Princes. Plus running around with that sword is always awesome.

If you're a high enough level however (I believe level 15 is required?) you can do this during Earth Patrol missions. From spawn, head left and you will see a small shack on it's own. In there, there are 3 Hive Majors (2 Acolytes and a Knight). After beating these three, head back up the way you came, and they should respawn.

The other alternative is the Summoning Pits, during the Phogoth the Untamed mission. Possibly more efficient, but I tend to steer clear of.. that... filthy no good -omitted-

Ahem. Sorry. Where was I?

Vex! There is a Minotaur Major in the Ember Caves you can find in the Venus patrol missions, all the way over next to the Pillar of Light past the bridge in the back corner of the structure. If you jump on your Sparrow, cross back under the bridge and cross to the other side of the area and return, he should have respawned. If not, try again and he will have the second time around (possibly just needed a second).

And finally, Cabal. Again, during the Mars Patrol, jump on a sparrow, and head straight. Go through the big tunnel straight ahead, then when you come out the other side, you should see an egg-shaped building. To the left of this should be a building marked "Clovis Bray". In here, you'll find an Imperial Phalanx Major. To make him respawn, simply run back outside, and across to the end of the walkway directly across from the entrance of this building, and he should respawn.