There are few potions that have little or no use in most situations. The accessibility and usefulness of potions cannot be understated. Most potions can be used by any character, with the only notable exceptions being giant strength, heroism, invulnerability, and super-heroism which can only be used by fighters. There is a full 20% chance of finding one or more potions using the random Magic Item generation tables in the DMG on page 121. Potions are one of the most common magic items found. I'll also touch on the creation of potions and why these should probably be some of the few easily-accessible magic items permitted for characters to create on their own. This article will seek to clear up all the rules concerning potions and their use in an AD&D campaign.
They are great for the DM in that most potions are single-use items, they have a limited duration, and the bonus gained is not absurdly powerful or overbalancing to the game.
These 'liquid spells' really are a life saver and can be extremely useful, but most potions are not overly powerful items, and as such are usually found by lower level characters with more frequency than, say, name level characters.
More likely than not, that first magic item is a potion. Nothing gets a new party more excited than their first magic items acquired in the game.
