These abilities activate when the Pokemon is in the first spot of the party:
Intimidate & Keen Eye: Decreases the chance of encountering lower-level wild Pokémon by 50%
Stench & White Smoke: Decreases the chances of encountering wild Pokémon (not just lower level) by 50%
Arena Trap & Illuminate: Increases the chance of encountering Pokémon to 200%.
No Guard - Increases the wild Pokémon encounter rate to 150%
Harvest: Increases the chance of running into Grass type Pokemon by 50% (in areas that have grass types)
Flash Fire: Increases the chance of running into Fire type Pokemon by 50% (in areas that have fire types)
Static and Lightning Rod: Increases the chance of running into Electric type Pokemon by 50% (in areas that have electric types)
Storm Drain: Increases the chance of running into Water type Pokemon by 50% (in areas that have Water types)
Magnet Pull: Increasess the chance of encountering wild Steel-type Pokémon by 50% (in areas that have them)
Synchronize: 50% chance that wild Pokémon encountered will have the same Nature as the Pokémon with Synchronize.
Cute Charm: Increases the chance to run into the opposite gender to 66.7%, regardless of normal gender ratios.
Compound Eyes: Increases the chance of wild Pokemon holding an item from 50%/5%/1% to 60%/20%/5%.
Swarm: Increases the chance of encountering wild Pokémon.
Suction Cups & Sticky Hold: Bites will occur more often while fishing.
Hustle, Pressure & Vital Spirit: Increases the chance to run into higher-level Pokemon.
Sand Veil: Decreases the wild Pokémon encounter rate by 50% in an area with a sandstorm
Snow Cloak: Decreases the wild Pokémon encounter rate by 50% in an area with a blizzard
Quick Feet - Decreases the wild Pokémon encounter rate.
Most if not all of the above abilities are still active even when the Pokemon is fainted.
Source
There's no held item that increases or decreases encounter rates
Also if a Pokemon is suggested in your Pokedex home screen, then it had a boosted chance of appearing in the area that it wants you to look for that Pokemon in. The selection of these Pokemon are semi-random, and unless you have a complete Pokedex, they will only show Pokemon that you have not caught before.
Also, apparently, according to Serebii, "If you find a rare Pokémon, or simply any Pokémon you're looking for, then when you defeat it, there is a slightly higher chance of seeing it again, so if you find a 1% Pokémon and want more of it, then it will start appearing more."
Source
