Potion

Potions are future craftable food items that confer specific effects in Minecraft. Potion recipes have not yet been defined as of the Beta 1.9 Pre-release. Potion effects were initially introduced in Beta 1.8. If Potions are hacked into the game and their damage value is changed, they will acquire effects.

History
Alchemy was first hinted at in July 2010, when Notch explained why redstone ore disintegrates into "dust". He states that dust will be used later in potions.

A couple months later, Notch did a Q&A session on Reddit. He was asked about Alchemy, and responded "Oh Yes! Definitely!". All of his posts in that thread are now deleted, but records can be found in other places.

Potion effects were introduced in Beta 1.8. Jeb later tweeted a screenshot showing potion durations and Glass Bottles taken from within from Beta 1.9 Pre-release 2.

Brewing
According to Jeb there are 161 possible potion combinations in Beta 1.9 Pre-release 2, and there will be 2,653 potions in the full Beta 1.9 release.

Trivia

 * Originally Potions were to be brewed in Cauldrons. Jeb later tweeted that both he and Notch had come up with a different way to brew potions, which was revealed to be Brewing Stands.
 * Taking a potion while already under the effects of another potion does not add onto the effects time, but simply resets it.
 * An Instant Damage III Potion is powerful enough to instantly kill its drinker
 * Once dead the effects of the potions go away.