Bulbasaur, Ivysaur and Venusaur
Squirtle, Wartortle and Blastoise
Charmander, Charmeleon and Charizard
Kabuto and Kabutops
Omanyte and Omastar
Mankey and Primeape
Growlithe and Arcanine
Teddiursa and Ursaring
Spinarak and Ariados
Gligar
Mantine
Articuno
Zapdos
Moltres
Mewtwo
Mew
Bulbasaur, Ivysaur and Venusaur
Squirtle, Wartortle and Blastoise
Charmander, Charmeleon and Charizard
Kabuto and Kabutops
Omanyte and Omastar
Vulpix and Ninetales
Meowth and Persian
Phanpy and Donphan
Ledyba and Ledian
Skarmory
Delibird
Articuno
Zapdos
Moltres
Mewtwo
Mew
All you need is a pokemon with the False Swipe attack. The Zangoose that you get from Zook has it by default. A pokemon with this move can almost always leave any opposing pokemon of lower level with 1 hit point, making it an easy target for pokeballs.
Go to Route 111, go to the sandstorm, and go all the way to the right. There you will find two fossils--the Claw Fossil and the Root Fossil. Pick one, then go to Rustboro City. Go to the president's office and go in a room with lots of scientists. Talk to the one in the lower right hand corner. Then...
At the sealed chamber midway between Pacifidlog and Slateport (accessible only from Pacifidlog) use Dive to enter a tunnel that leads to a slab with braille. Surface there and enter the sealed chamber. The next step is to go to the back of that room and use Dig on the space where you see braille in ...
In the Shoal Cave north of the hunter's house is Shoal Stone and Shoal Sand. The sand is easy to find in mounds but you have to wait for the tide to get the stone. Randomly you'll find a Shiny Spheal.
You can get "free" time in the safari zone by simply not moving from the area where your target pokemon is. Stand on one square in that zone and lightly tap the D-pad to change the character's facing. Each facing doesn't count towards the step-limit but will count for having an encounter.
Become the pokemon league champion.
Complete your Pokedex.
Beat 50 trainers in the battle tower.
Receive a ribbon from all five contest types in the master ranking.