I caught Palkia in the fourth Premier Ball I threw.
Uxie broke out of 10 Premier Balls, a Dusk Ball, an Ultra Ball, and about 30 Pokeballs before I finally caught it (in the Pokeball)
Azelf did the same thing, but I didn't have any Premier Balls left at this point, so I just lobbed Pokeballs until I got it (it took about 30 or 40)
I have yet to get Mesprit or any other legends (but I did get Rotom in the third or fourth Premier Ball I threw, and a Beldum in about 5 Pokeballs)
As you can tell, I don't like using things other than Pokeballs and Premier Balls. The only things I caught with something better are a Chimecho with an Ultra, and about 5 random things with Greats.