I want to discuss what items should be included in a "useful items" list in this topic. Most of it seems obvious, but some will definitely be up for debate.
TMs aren't included here because TMs can only be replaced by other TMs and that isn't going to change.
- All types of Poke Balls, except for the game's Safari Ball / Park Ball / etc
- All direct healing items including herbs (more on berries a few lines down)
- All traditional battle items (X items, Guard Spec/Dire Hit, Poke Doll/Fluffy Tail, Flutes)
- All items that can be sold to a regular shop for P500 or more (lets you get useful items)
- Held items with an in-battle use (except for the EV-doubling ones) that don't discriminate based on type or species (e.g. Choice Specs, King's Rock, Amulet Coin)
- Evolution stones
- Field-use items (Repels & Escape Rope)
- Heart Scales
- All berries that cure HP/PP or cure status directly (how many times has the Bitter Berry / Persim Berry saved a glitchless speedrun? Statuses are less predictable in randomizers, but it's still nice to have insurance against them)
- Type-specific held items (can often be useful, if a little situational. Quite a few are covered by the price clause anyway)
- EV-reducing berries
- Berries that do something when HP falls into critical (too situational)
- Wings (from Gen5) - 1 EV is useless in all but the craziest of situations
- Fossils (when they're consumable in Gen5) - revival place is too out-of-the-way
- Pokemon-specific held items - way too situational
- Specific evolution items - debatable, but very situational. There's no way you should be holding out to find the specific item for your particular Pokemon anyway.
- Gems - these are like type-specific held items but even more situational. The chances of getting one when you can actually use it to clutch a situation are slim to none.
- Mail - lol
- Apricorns - no time to wait for one day in a speedrun
- Berries without an in-battle effect - no Pokeblocks needed