Location: Route 101

The first Pokémon you get given are the starter Pokémon. In this game, they are Treecko, Torchic and Mudkip. In this game, you recieve them when you encounter Professor Birch in Route 101, where he asks you to use one to help defend him against a Poochyena.

Location: Slateport City

When you get to Slateport City, you get given the opportunity to participate in Pokémon Contests. After you have participated in your first one, a Pokémon Breeder will take you aside for a moment and offer you the special Pikachu which has clothes to match your Contest Clothes, Rock Star Pikachu if you're male or Pop Star Pikachu if you're female. This Pikachu has its Hidden Ability. In addition to that, it also has high stats for each of the Contest Types.

Location: Lavaridge Town

The next gift is given in Lavaridge Town by the old woman near the hot springs. She will give you an Egg which, when hatched, will give you a Wynaut, which cannot be found in the wild.

Location: Southern Island

The next gift is given in Southern Island. As you reach Route 118, a Latias/Latios will appear to you and Steven and take you to the island where you discover Team Magma/Aqua are trying to take it and its Mega Stone. After defeating them, Latios or Latias will join you in Omega Ruby and Alpha Sapphire respectively. They come holding their Mega Stone.

Location: Weather Institute

After you have saved the people in the Weather Institute from Team Magma or Team Aqua, the scientists within the Weather Institute will give you the Pokémon Castform, which cannot be found in the wild.

Location: Route 101

The next Pokémon you get given even more starter Pokémon. After the completion of the Elite Four, when you next exit your house in Littleroot Town, Professor Birch will call you over and tell you that he is under attack, this time from a Shroomish. He will ask for you to help him using Pokémon in his bag, this time giving you a choice between the Johto starters.

Location: Route 101

The next Pokémon you get given are even more starter Pokémon. After the completion of the Delta Episode, when you next exit your house in Littleroot Town, Professor Birch will call you over and tell you that he is under attack, this time from a Machoke from the Delivery services which he misconstrued the intent. He will ask for you to help him using Pokémon in his bag, this time giving you a choice between the Unova starters.

Location: Route 101

The next Pokémon you get given are even more starter Pokémon. After the completion of the Elite Four again, when you next exit your house in Littleroot Town, Professor Birch will call you over and tell you that he is under attack, this time it seems he mistook his wife for a wild Pokémon. He will ask for you to help him using Pokémon in his bag, this time giving you a choice between the Sinnoh starters.

Location: Lavaridge Town

The next gift is given in Lavaridge Town by the old woman near the hot springs. After beating Primal Groudon/Kyogre, she will give you another Egg which, when hatched, will give you a Togepi, which cannot be found in the wild.

Location: Mossdeep City

After you have completed the Delta Episode, if you return to Steven Stone's house in Mossdeep City, you will find a PokéBall on the table with a note saying that the Beldum is a gift for you.

Location: Battle Resort

After you have completed the Delta Episode, you gain access to the Battle Resort. In the island area, in the first Beach House on the right, you will find a pair of grunts, one from each team. They will tell you that they have deserted their team to be with eachother, but other grunts arrive and tell them the transpirings. When you next return to the hut, both grunts will say that they are going to go back to the teams to help change them and will both offer you a Pokémon.