Latios & Latias:
First, beat the game. Then purchase the friend area, southern island. Also get surf in solar cave and sleep. Then when you wake up, Latios will steal TMs and go to the Northern Range. You go there and complete the dungeon. Then you see latios but wont have to fight it. It comes to town square and tellls you that his sister latias is injured and is at Pitfall Valley. You go there and complete that dungeon. Latias is there and you don't have to fight it. The latios and latias is reunited. Then they agree to join your rescue team.
In order to get Mewtwo, you must first recruit all the other legendary pokemon (Ho-oh, Entei, Raikou, Suicune, Zapdos, Articuno, Moltres, Kyogre, and Groudon). Mewtwo is in the Western Cavern on floor 99. You'll have to beat him using only one pokemon, and he's got around 900 HP.
If you don't want to run around in dungeons for XP, go to the Makuhita Dojo and fight Team Hydro. They're worth 5000 XP each time.
Enter the following Wonder Mail passwords to obtain some secret missions. These codes work with either version of the game, but you must have access to the mission's dungeon for them to work. Feel free to submit your own!
Meet with Minun:
Enter f?rpf?...??+7?ct?h64?0r??? as a password. The reward is a 400 Poke and a Heal Ribbon. Note the ellipse (...) is entered as a single character, not three.
I'm So Worried About Ninoran:
Enter 1??94wt?0f9jnf?97770+8?w as a password. The reward is 500 Poke.
Enter 4?mf87t??3n4[Female]r?2-?6r8c?? as a password. The reward is a Max Elixir. [Female] refers to the single-character female sign.
Help I Can't Exit:
Enter ??-fh?f??3p?q??+8?76T8?? as a password. The reward is TM 31 and 200 Poke.
Enter ??-FH?F??3P?Q??+8?76t8?? as a password. Not sure about this reward...
Blue Plains Friend Area mission:
Enter 5?2YQW0??T0QJC?[Male]FH16WR?W as a password. [Male] refers to the male sign, a single character. The mission will allow you access to the Blue Plains friend area.
Stormy Sea mission:
Enter X??S??X?468?*+??9756SY?? as a password. The quest rewards you with 400 poke and a magicarp (blue version) or a trawl orb and a feebas (red version).
Enter ??F(...) [Male]2S? 4R73 S0?7 64NR J7?W as a password.
Thanks to Revolution Readers pokemon master, evanm, Timmers, and Mister-ball!