Because the other answers were just links, I've decided to post a whole list.
Note: I'm only listing their effects when used on or held by (depending on the Berry) Pokémon, not in Pokéblocks/Poffins, nor their effect when the holder uses Natural Gift, Fling, ect., which is why some Berries say they have no effect.
Regular Berries
Cheri Berry - Cures paralysis
Chesto Berry - Cures sleep
Pecha Berry - Cures poison
Rawst Berry - Cures burn
Aspear Berry - Cures freeze
Leppa Berry - Restores 10 PP of a selected move
Oran Berry - Restores 10 HP
Persim Berry - Cures confusion
Lum Berry - Cures burn, freeze, poison, bad poison, paralysis, sleep, and confusion
Sitrus Berry - Heals 30 HP in Gen 3, and 25% in Gen 4 onwards
Figy Berry - When the holder's HP falls below 25%, it restores 50% HP in Gen 7, and 33% HP in Gen 8, but confuses the holder if it dislikes spicy food (restores 12.5% HP when below 50% HP before Gen 7)
Wiki Berry - When the holder's HP falls below 25%, it restores 50% HP in Gen 7, and 33% HP in Gen 8, but confuses the holder if it dislikes dry food (restores 12.5% HP when below 50% HP before Gen 7)
Mago Berry - When the holder's HP falls below 25%, it restores 50% HP in Gen 7, and 33% HP in Gen 8, but confuses the holder if it dislikes sweet food (restores 12.5% HP when below 50% HP before Gen 7)
Aguav Berry - When the holder's HP falls below 25%, it restores 50% HP in Gen 7, and 33% HP in Gen 8, but confuses the holder if it dislikes bitter food (restores 12.5% HP when below 50% HP before Gen 7)
Iapapa Berry - When the holder's HP falls below 25%, it restores 50% HP in Gen 7, and 33% HP in Gen 8, but confuses the holder if it dislikes sour food (restores 12.5% HP when below 50% HP before Gen 7)
Razz Berry - In Let's Go, Pikachu! and Let's Go, Eevee!, it makes wild Pokémon more likely to be captured
Bluk Berry - None
Nanab Berry - In Let's Go, Pikachu! and Let's Go, Eevee!, it makes wild Pokémon move less
Wepear Berry - None
Pinap Berry - In Let's Go, Pikachu! and Let's Go, Eevee!, it makes wild Pokémon more likely to drop items
Pomeg Berry - Lowers HP EVs by 10, and also raises friendship in Emerald and Gen 4 onward
Kelpsy Berry - Lowers Attack EVs by 10, and also raises friendship in Emerald and Gen 4 onward
Qualot Berry - Lowers Defense EVs by 10, and also raises friendship in Emerald and Gen 4 onward
Hondew Berry - Lowers Special Attack EVs by 10, and also raises friendship in Emerald and Gen 4 onward
Grepa Berry - Lowers Special Defense EVs by 10, and also raises friendship in Emerald and Gen 4 onward
Tamato Berry - Lowers Speed EVs by 10, and also raises friendship in Emerald and Gen 4 onward
Cornn Berry - None
Magost Berry - None
Rabuta Berry - None
Nomel Berry - None
Spelon Berry - None
Pamtre Berry - None
Watmel Berry - None
Durin Berry - None
Belue Berry - None
Occa Berry - Halves the damage taken by the holder from a super effective Fire-type move
Passho Berry - Halves the damage taken by the holder from a super effective Water-type move
Wacan Berry - Halves the damage taken by the holder from a super effective Electric-type move
Rindo Berry - Halves the damage taken by the holder from a super effective Grass-type move
Yache Berry - Halves the damage taken by the holder from a super effective Ice-type move
Chople Berry - Halves the damage taken by the holder from a super effective Fighting-type move
Kebia Berry - Halves the damage taken by the holder from a super effective Poison-type move
Shuca Berry - Halves the damage taken by the holder from a super effective Ground-type move
Coba Berry - Halves the damage taken by the holder from a super effective Flying-type move
Payapa Berry - Halves the damage taken by the holder from a super effective Psychic-type move
Tanga Berry - Halves the damage taken by the holder from a super effective Bug-type move
Charti Berry - Halves the damage taken by the holder from a super effective Rock-type move
Kasib Berry - Halves the damage taken by the holder from a super effective Ghost-type move
Haban Berry - Halves the damage taken by the holder from a super effective Dragon-type move
Colbur Berry - Halves the damage taken by the holder from a super effective Dark-type move
Babiri Berry - Halves the damage taken by the holder from a super effective Steel-type move
Chilan Berry - Halves the damage taken by the holder from a Normal-type move
Liechi Berry - Raises the holder's Attack by one stage when its HP falls below 25%
Ganlon Berry - Raises the holder's Defense by one stage when its HP falls below 25%
Salac Berry - Raises the holder's Speed by one stage when its HP falls below 25%
Petaya Berry - Raises the holder's Special Attack by one stage when its HP falls below 25%
Apicot Berry - Raises the holder's Special Defense by one stage when its HP falls below 25%
Lansat Berry - Raises the holder's critical hit ratio when its HP falls below 25%
Starf Berry - Raises one of the holder's stats, selected at random, by two stages when its HP falls below 25%
Enigma Berry - Restores a quarter of the holder's max HP if it's hit by a super effective move
Micle Berry - In Gen 4, the holder's next move will ignore accuracy and evasion, and non-OHKO moves have a chance to break through Protect and Detect, when its HP falls below 25%, and in Gen 5, it raises the accuracy of the next move by 20% when the holder's HP falls below 25%
Custap Berry - Makes the holder goes first when its HP falls below 25%
Jaboca Berry - If the holder is hit with a physical move, the attacker loses 12.5% of its max HP
Rowap Berry - If the holder is hit with a special move, the attacker loses 12.5% of its max HP
Roseli Berry - Halves the damage taken by the holder from a super effective Fairy-type move
Kee Berry - Raises the holder's Defense by one stage if it's hit by a physical move
Maranga Berry - Raises the holder's Special Defense by one stage if it's hit by a special move
Let's Go, Pikachu! and Let's Go, Eevee!-exclusive Berries
Silver Razz Berry - Makes wild Pokémon more likely to be captured, more effective than the regular Razz Berry
Silver Nanab Berry - Makes wild Pokémon move less, more effective than the regular Nanab Berry
Silver Pinap Berry - Makes wild Pokémon more likely to drop items, more effective than the regular Pinap Berry
Golden Razz Berry - Makes wild Pokémon more likely to be captured, more effective than the Silver Razz Berry
Golden Nanab Berry - Makes wild Pokémon move less, more effective than the Silver Nanab Berry
Golden Pinap Berry - Makes wild Pokémon more likely to drop items, more effective than the Silver Pinap Berry
Gen 2-exclusive Berries
Berry - Restores 10 HP
Gold Berry - Restores 30 HP
MysteryBerry - Restores 5 PP
MiracleBerry - Cures burn, freeze, poison, bad poison, paralysis, sleep, and confusion
Mint Berry - Cures sleep
Burnt Berry - Cures freeze
Ice Berry - Cures burn
Bitter Berry - Cures confusion
PRZCureBerry - Cures paralysis
PSNCureBerry - Cures poison
e-Reader Berries
Pumkin Berry - Cures freeze
Drash Berry - Cures poison
Eggant Berry - Cures infatuation
Strib Berry - None
Chilan Berry - None
Nutpea Berry - None
Ginema Berry - Raises a lowered stat in battle
Kuo Berry - None
Yago Berry - Cures Burn
Touga Berry - Cures confusion
Niniku Berry - None
Topo Berry - None
Source: Bulbapedia
