What legendary Pokemon can catch in Pokemon emerald?

Answer 1

You can capture Registeel, Regice, Regirock, Rayquaza, Groudon, Kyogre (2 of them to be specific), Latios/Latias (after beating the Pokemon league choosing blue or red after watching TV determines what Lati you get).

Answer 2

you can get lugia ho-oh latios or latias mew deoyxs rayquaza kyorge groundon

for lugia and ho-oh you need a mystic ticket to go to navel rock

for mew you need a old sea map to go to faraway island

for deoyxs you need a aurora ticket

for latios and latias u get them after you beat the elite 4 or you get a eon ticket but you can only choose one to catch

for rayquaza u go to the sky pillar

for kyorge u go to marine cave

for groundon u go to terra cave