As it's debatable on which items are useful or not in Emerald, this list includes all items that can be stolen by Thief or Covet:
Wild Pokémon
Note that this list excludes all Pokémon that cannot be naturally found in the wild (Pokémon that only evolve from their pre-evolutions, gift Pokémon, etc.) or those found in Battle Facilities.
Berries
Oran Berry — 100% on Shuckle, 50% on Pikachu, Linoone, 5% on Zigzagoon
Rawst Berry — 100% on Vulpix, Numel
Lum Berry — 100% on Mew
Persim Berry — 5% on Girafarig, Kecleon
Pecha Berry — 5% on Poochyena, Mightyena
Sitrus Berry — 5% on Linoone
Chesto Berry — 5% on Whismur, Loudred, Spinda
Leppa Berry — 5% on Skitty
Evolution items
Metal Coat — 5% on Magnemite, Magneton
Dragon Scale — 5% on Horsea, Bagon
King's Rock — 5% on Hariyama
Sun Stone — 5% on Solrock
Stat-enhancing items
Light Ball — 5% on Pikachu
Metal Powder — 5% on Ditto
Type-enhancing items
Twisted Spoon — 5% on Abra
Sharp Beak — 5% on Doduo, Dodrio
Hard Stone — 5% on Aron, Lairon
Poison Barb — 5% on Roselia, Cacnea
Soft Sand — 5% on Trapinch
Spell Tag — 5% on Shuppet, Banette, Duskull
Valuable Items
Nugget — 5% on Grimer
Star Piece — 5% on Staryu
Stardust — 50% on Staryu
Yellow Shard — 5% on Chinchou
Red Shard — 5% on Corsola
Big Pearl — 5% on Gulpin
Blue Shard — 5% on Clamperl
Green Shard — 5% on Relicanth
Heart Scale — 50% on Luvdisc
Miscellaneous held items
Quick Claw — 5% on Sandshrew
Everstone — 5% on Geodude, Graveler
Smoke Ball — 5% on Koffing
Medicine
Moomoo Milk — 100% on Miltank
Sacred Ash — 100% on Ho-oh
Pokémon italicized are found only in the Safari Zone, and therefore cannot be naturally battled. Items that are italicized similarly cannot be obtained from a Pokémon if not from the Safari Zone.
Trainer Battles
This list excludes trainers found in the Battle Facilities.
Berries
Oran Berry — Pokéfan Miguel's Skitty (Initial battle, first and second rematch) and Delcatty (third rematch) on Route 103, Pokéfan Isabel's Minun and Plusle (initial battle, first, second and third rematch) on Route 110, Pokéfan Kaleb's Minun and Plusle on Route 110, Pokéfan Vanessa's Pikachu on Route 121, Gym Leader Roxanne's Nosepass (Gym Battle), Gym Leader Winona's Altaria (Gym Battle)
Sitrus Berry — Pokéfan Miguel's Delcatty (Fourth Rematch onwards) on Route 103, Pokéfan Isabel's Minun and Plusle (Fourth Rematch onwards) on Route 110, Gym Leader Roxanne's Kabuto (First Rematch), Nosepass (First Rematch onwards), and Kabutops (Second Rematch onwards), Gym Leader Brawly's Makuhita (Gym Battle), Hariyama (First Rematch onwards), and Machamp (First Rematch onwards), Gym Leader Wattson's Manectric (Gym Battle onwards) and Magneton (First Rematch onwards), Gym Leader Norman's Slaking (Gym Battle onwards) and Gym Leader Norman's Slaking ×2 (First Rematch onwards), Gym Leader Winona's Dratini (First Rematch), Dragonair (Second and Third Rematch), and Dragonite (Fourth Rematch onwards), Gym Leaders' Tate and Liza's Lunatone (Gym Battle) and Solrock (Gym Battle onwards), Elite Four member Sidney's Absol, Elite Four member Phoebe's Dusclops, Elite Four member Glacia's Walrein, Elite Four member Drake's Salamence, Champion Wallace's Milotic, Steven Stone's Metagross at Meteor Falls
Chesto Berry — Gym Leader Winona's Altaria (First Rematch onwards), Gym Leaders' Tate and Liza's Lunatone and Xatu (First Rematch onwards), Gym Leader Juan's Kingdra (Gym Battle onwards) and Crawdaunt (First Rematch onwards)
Type-enhancing items
Dragon Fang — Dragon Tamer Nicolas' Shelgon (Fourth Rematch onwards)
Black Belt — Black Belt Nob's Machamp (Fourth Rematch onwards)
SilverPowder — Bug Maniac Jeffrey's Masquerain (Fourth Rematch onwards)
Valuable Items
Nugget — Rich Boy Winston's Zigzagoon/Linoone on Route 104, Lady Cindy's Zigzagoon/Linoone on Route 104, Lady Sarah's Zigzagoon on Route 116, Rich Boy Dawson's Zigzagoon on Route 116
Miscellaneous held items
White Herb — Gym Leader Flannery's Torkoal (Gym Battle onwards), Gym Leader Flannery's Camerupt and Magcargo (First Rematch onwards)
Source
