There are many trash cans with items in them. Here's the list I came up with:
Red/Blue/Yellow:
S.S. Anne- Great Ball in the lowest trash can in the kitchen.
Gold/Silver/Crystal:
Celadon City: In the restaurant, the trash has Leftovers.
Ruby/Sapphire/Emerald:
S.S. Tidal: Leftovers in the trash can in the storage.
Abandoned Ship- Room 6 Key in Room 4, hidden in the trash can.
FireRed/LeafGreen:
S.S. Anne- Hyper Potion on B1F lower right corner; Chesto Berry on lowest trash can in kitchen; Cheri Berry on middle trash can in kitchen; Pecha Berry on the upper trash can.
Diamond/Pearl/Platinum:
Hotel Grand Lake- Max Revive inside a trash can in the bungalow to the northeast of the hotel entrance (requires Rock Climb).
Old Chateau- Antidote on 1F Dining Area, in the northern trash can on the west side (D/P only).
Pokémon Mansion- Trash can in the first room left from the entrance: Burn Heal (D/P), Protein (Platinum).
Black/White:
Village Bridge- Leftovers in the trash can under bridge.
Black 2/White 2:
Virbank city- Antidote in a trash can on the west side of the blue house south of the Pokémon Center
Nimbasa city- Revive In the trash can near the Rondez-View Ferris Wheel
Pokémon World Tournament- Zinc in the trash can near the fountain
Mistralton city- Iron in the trash can in house near Pokémon Center
Humilau city- Full Restore in the trash can of the hut containing the Roughneck who wants a Mantine
Twist Mountain- Full Restore in the trash can next to the Vending Machine (only during Spring/Summer/Autumn)
Accumula Town- Max Repel in the trash can near the benches.
Village Bridge- PP Up in the trash can in the northwest corner.
X/Y
If you like trash can items, Kalos is the greatest place to go in the Pokemon World.
There are a lot of items (and Pokémon) you can find in shaking trash cans here.
Lost Hotel:
Daily trash can
Escape Rope Often in a trash can after a shadow leaps out
Super Repel Often in a trash can after a shadow leaps out
Max Elixir Rarely in a trash can after a shadow leaps out
Dusk Ball Often in a trash can after a shadow leaps out
HP Up Sometimes in a trash can after a shadow leaps out
Protein Sometimes in a trash can after a shadow leaps out
Iron Sometimes in a trash can after a shadow leaps out
Tuesday trash cans
Escape Rope Often in a trash can after a shadow leaps out
Max Repel Often in a trash can after a shadow leaps out
Nugget Often in a trash can after a shadow leaps out
Big Nugget Rarely in a trash can after a shadow leaps out
Calcium Sometimes in a trash can after a shadow leaps out
Zinc Sometimes in a trash can after a shadow leaps out
Carbos Sometimes in a trash can after a shadow leaps out
Pokémon Village:
Daily trash can
Honey Often in a trash can after a shadow leaps out
Poké Toy Sometimes in a trash can after a shadow leaps out
Pretty Wing Often in a trash can after a shadow leaps out
Tiny Mushroom Often in a trash can after a shadow leaps out
Big Mushroom Sometimes in a trash can after a shadow leaps out
Max Revive Sometimes in a trash can after a shadow leaps out
Mental Herb Sometimes in a trash can after a shadow leaps out
Thursday trash cans
Honey Often in a trash can after a shadow leaps out
Prism Scale Often in a trash can after a shadow leaps out
Big Mushroom Often in a trash can after a shadow leaps out
Balm Mushroom Sometimes in a trash can after a shadow leaps out
Eviolite Rarely in a trash can after a shadow leaps out
Heal Powder Sometimes in a trash can after a shadow leaps out
Revival Herb Sometimes in a trash can after a shadow leaps out
Pikachu/Eevee:
S.S. Anne- Tiny Mushroom on the lowest kitchen trash can.
Sword/Shield:
Motostoke City- Pokeball: Lower tier, in the trash bin on the lower east side (reappears daily)
Brilliant Diamond/Shining Pearl:
Old Chateau- Antidote on 1F Dining Area, in the northern trash can on the west side.
Pokémon Mansion- Burn Heal in the trash can in the first room left from the entrance.
No surprise there, BDSP seems to copy Diamond and Pearl more than any other Pokémon remake.
...Bulbapedia's BDSP location data is incomplete still, so there may be some I missed, as that's where all of my info came from.
(Source: Bulbapedia and strategy wiki)