Abilities:
Arena Trap- Increases wild Pokemon encounter rate by 100% if the lead Pokemon has this ability
Compound Eyes- Increases the chance of a wild Pokemon holding an item if the lead Pokemon has this ability
Cute Charm- Increases the chance of a wild Pokemon to be of the opposite gender as the Pokemon with this ability by 66.7% if it's in the lead slot
Flame Body- Halves the amount of steps required to hatch an egg
Honey Gather- The Pokemon has a chance to obtain Honey after winning a battle
Hustle- Increases the chance of finding a high leveled wild Pokemon by 50% if the lead Pokemon has this ability
Hyper Cutter (Only in Pokemon Emerald)- If the Pokemon with this ability uses Cut on any tall grass, it will cut all tall grass within a two square radius of the player. Due to Gen IV and all subsequent generations scrapping the idea of cutting tall grass, Hyper Cutters overworld effect became obsolete and thus was also done away with.
Illuminate- Increases wild Pokemon encounter rate by 100% if the lead Pokemon has this ability
Immunity- The Pokemon cannot take poison damage in the overworld
Intimidate- Any wild Pokemon that are 5 levels or lower than the level of the Pokemon with this ability has its encounter rate halved if the lead Pokemon has this ability
Keen Eye- Any wild Pokemon that are 5 levels or lower than the level of the Pokemon with this ability has its encounter rate halved if the lead Pokemon has this ability
Lightning Rod (Only in Pokemon Emerald)- Trainers registered with the PokeNavs Match Call will call more often if the lead Pokemon has this ability. Due to the Match Call and PokeNav both being scrapped in subsequent generations, Lightning Rods overworld effect was also done away with.
Magma Armor- Halves the amount of steps required to hatch an egg
Magnet Pull- Makes encountering Steel types 50% more likely if Steel types can be found in the area if the lead Pokemon has this ability
No Guard- Increases wild Pokemon encounter rate by 50% if the lead Pokemon has this ability
Pickup- Any Pokemon with this ability has a 10% chance of obtaining an item after winning a battle
Pressure- Increases the chance of finding a high leveled wild Pokemon by 50% if the lead Pokemon has this ability
Quick Feet- Halves the encounter rate of all wild Pokemon if the lead Pokemon has this ability
Sand Veil- Halves the encounter rate of all wild Pokemon in an area where a sandstorm is occurring in the overworld (such as Route 111 in Hoenn) if the lead Pokemon has this ability
Snow Cloak- Halves the encounter rate of all wild Pokemon in an area where it is hailing in the overworld (such as Route 217 in Sinnoh) if the lead Pokemon has this ability
Static- Makes encountering Electric types 50% more likely if Electric types can be found in the area if the lead Pokemon has this ability
Stench- Halves the encounter rate of all wild Pokemon if the lead Pokemon has this ability
Sticky Hold- Makes bites more likely to occur while fishing if the lead Pokemon has this ability
Suction Cups- Makes bites more likely to occur while fishing if the lead Pokemon has this ability
Swarm- Increases wild Pokemon encounter rate by 100% if the lead Pokemon has this ability
Synchronize- Makes it 50% more likely that the wild Pokemon (barring roaming legendarys and Fossils) will have the same Nature as the Pokemon with this ability if its in the lead slot. From ORAS onwards, it also makes gift Pokemon that are in the Undiscovered Egg Group (except for Mystery Gift Pokemon) always have the same Nature as the Pokemon with Synchronize if its in the lead slot.
Vital Spirit- Increases the chance of finding a high leveled wild Pokemon by 50% if the lead Pokemon has this ability
White Smoke- Halves the encounter rate of all wild Pokemon if the lead Pokemon has this ability
Moves:
Chatter (Only in Genrations IV and V)-* Can be used to record audio, which will play back every time as Chatot's new cry as well as when it uses Chatter until it gets deposited in the PC
Cut- Can be used to cut down certain trees, as well as tall grass in Gens I-III.
Defog (Only in Gen IV)- Clears away any overworld fog
Dig- If used in a cave or certain buildings (like Gyms), the player is transported to the entrance of the cave/building
Dive (Only in Gens III, V, and VI)-* Allows the player to go underwater when they are on a dark tile of water while surfing
Flash- Illuminates particularly dark caves
Fly- Allows players to travel to any city they have already visited
Headbutt (Only in Gens II and IV)- Lets the player headbutt certain trees to potentially find wild Pokemon
Milk Drink- Can be used outside of battle to take away 20% of the users HP and use it to restore another party members HP by the same amount of points
Rock Climb (Only in Gen IV)- Lets the player climb rocky surfaces
Rock Smash (Only in Gens II, III, IV, and VI)- Lets the player break certain types of rocks to clear paths and potentially find wild Pokemon or items
Secret Power (Only in Gens III and VI)- Can be used on some bushes, trees, and rock walls to create a Secret Base
Softboiled- Can be used outside of battle to take away 20% of the users HP and use it to restore another party members HP by the same amount of points
Strength- Can be used to push certain boulders in the overworld
Surf- Can be used to travel over bodies of water
Sweet Scent- When used in tall grass, caves, or other places where Pokemon can be found in clear weather in Gens II-V, it will always initiate a wild Pokemon battle without fail. In Gen VI, under the same conditions, it will always initiate a Horde Battle without fail
Teleport- Warps the player to the last place their Pokemon were healed at
Waterfall (Only in Gens II-VI)- Allows the player to climb up waterfalls while surfing
Whirlpool (Only in Gens II and IV)- Allows the player to traverse over whirlpools while surfing
*- Starting Gen VII, there are no longer any moves that have field effects
Sources: This and this
Hope I could help!
