Arena Trap (ability) – From Pokémon Emerald onwards, if the Pokémon with Arena Trap is leading the party, then the wild Pokémon encounter rate is increased to 200%.
Compoundeyes (ability) – In Pokémon Emerald and all subsequent games, if the Pokémon with the ability leads the party, even if it has fainted, the chance of finding a Pokémon in the wild holding an item increases by 50%.
Cute Charm (ability) – From Pokémon Emerald onwards, if the Pokémon with Cute Charm is first in the party, the chance of encountering a Pokémon of the opposite gender is 66.7%, regardless of gender ratios. This does not affect the swarming Pokémon species.
Flame Body (ability) – In Pokémon Emerald and all subsequent games, it also halves the number of steps it takes for an egg to hatch. Both the Pokémon with Flame Body and the egg must be in the party in order for this to work. Magma Armor also has a similar effect. However this effect will not stack up if multiple Pokémon with Flame Body and Magma Armor are in the party.
Headbutt (move) – In Generation II, Headbutt was introduced as a move which can be used out of battle, allowing the player to shake small trees, sometimes causing a wild Pokémon to drop out. Depending on the time of day, the Pokémon which falls out may be asleep. Some Pokémon can only be caught by this method (e.g Pineco, Heracross) as well as being found in trees in certain areas. In HeartGold and SoulSilver, as with Generation II, the ability to use Headbutt on trees in the field has returned. However, the only change is that Pokémon will not be sleeping when they are encountered, regardless of the time of day. After the National Pokédex is acquired, non-regional Pokémon from Hoenn or Sinnoh can also be found using this method.
Honey Gather (ability) – Pokémon with Honey Gather may collect Honey after a battle, as long as the Pokémon is not holding a held item. See also Pickup.
Hustle (ability) – From Pokémon Emerald onwards, if the Pokémon with Hustle is leading the party, then Hustle increases the chance of battling a higher-leveled wild Pokémon by 50%.
Hyper Cutter (ability) – In Pokémon Emerald, using Cut will remove all tall grass within a two square radius of the player’s position, as opposed to a one square radius without this ability. In Generation IV, Hyper Cutter has no effect outside of battle due to removal of cutting tall grass.
Illuminate (ability) – If the Pokémon with Illuminate is leading the party, then the wild Pokémon encounter rate is increased to 200%.
Intimidate (ability) – From Pokémon Emerald onwards, if the Pokémon with Intimidate is leading the party, Intimidate decreases the chance of encountering a lower-level wild Pokémon by 50%. See also Keen Eye.
Keen Eye (ability) – From Pokémon Emerald onwards, if the Pokémon with Keen Eye is leading the party, then Keen Eye decreases the chance of encountering a lower-level wild Pokémon by 50%. See also Intimidate.
Lightningrod (ability) – In Pokémon Emerald, Trainers registered with the PokéNav’s Match Call function will call more often if a Pokémon with Lightningrod leads the party.
Magma Armor (ability) – In Pokémon Emerald and all subsequent games, Magma Armor halves the number of steps it takes for a Pokémon egg to hatch, provided that the Pokémon with Magma Armor and the egg are both in the party. All eggs that are in the party at the time are affected. This effect will not stack up if multiple Pokémon with Magma Armor are in the party, nor will it stack up if a Pokémon with Flame Body, which also has a similar effect, is in the party.
Magnet Pull (ability) – From Pokémon Emerald onwards, if the Pokémon with Magnet Pull is leading the party, then the likelihood of encountering wild Steel-type Pokémon is increased by 150%.
Milk Drink (move) – Similar to Softboiled, Milk Drink can also be used outside of battle to take away some HP from the user and restore another party Pokémon’s HP.
No Guard (ability) – Outside of battle, if the Pokémon with No Guard is leading the party, then No Guard increases the wild Pokémon encounter rate.
Pickup (ability) – Pickup allows the player to receive free items. After a battle, any Pokémon on the team that has this ability and is not already holding an item has a 10% chance of picking up an item. It can be retrieved through the normal means of taking a held item.
Pressure (ability) – From Pokémon Emerald onwards, if the Pokémon with Pressure is leading the party, then Pressure increases the chance of battling a higher-leveled wild Pokémon by 50%. See also Hustle and Vital Spirit.
Secret Power (move) – In Ruby, Sapphire and Emerald, Secret Power allows the user to create their own secret base. When used on certain trees, a vine drops down. When used on indented walls, a cave opens. When used on certain bushes, an entrance opens.
Snow Cloak (ability) – If the Pokémon with Snow Cloak is leading the party in an area with a blizzard, then Snow Cloak decreases the wild Pokémon encounter rate by 50%.
Softboiled (move) – Similar to Milk Drink, Softboiled can also be used outside of battle to take away some HP from the user and restore another party Pokémon’s HP.
Suction Cups (ability) – From Pokémon Emerald onwards, if a Pokémon with Suction Cups is in first place in the player’s party bites will occur more often while fishing.
Sweet Scent (move) – Sweet Scent causes wild Pokémon to appear in clear weather conditions while standing.
Synchronize (ability) – From Emerald onwards, if the Pokémon with this ability is leading the party, Synchronize gives a 50% chance of encountering a wild Pokémon with the same nature. However, this does not apply to any Pokémon created with Method 1 of the random number generator. This includes Emerald’s ‘one-off’ Pokémon such as legendaries, Castform, and Beldum, as well as Generation IV’s roaming legendaries and its non-legendary one-offs, including Bebe’s Eevee and the Porygon in Veilstone City.
Teleport (move) – Teleport warps the player to the last healing spot visited (a Pokémon Center, the player’s home, etc.).
White Smoke (ability) – From Pokémon Emerald onwards, if the Pokémon with White Smoke is leading the party, then White Smoke decreases the wild Pokémon encounter rate by 50%.
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Hope I helped!