If you're an alchemist, you either love the discovery system – or you despise it and wish to blast it back to the depths of Developers' Hell (that's one of those rock-and-lava zones, right?). Implemented with The Burning Crusade expansion, the discovery system gives alchemists a small (err, very small ... ok, very, very small ... ok, infinitesimally small) chance of discovering a new recipe every time they make a potion, elixir or flask. Players seem split between considering it a creative new mechanic or an annoying contrivance and roadblock, but after several patches and adjustments, the system seems here to stay.
Let's jump right in with your most burning question: Just how small (err, very small ... ok, very, very small ... ok, infinitesimally small) actually are your chances for making a discovery? Pretty darn small. Prior to patch 2.1, the most commonly cited figure floating around was 0.01%. (Discoveries were disabled via hot-fix for a short time just before patch 2.1, reportedly to prevent an exploit in which alchemists who repeatedly tried to create potions with no bag space could make discoveries without actually creating a potion or using potion ingredients.)
In patch 2.1, Blizzard noted that discovery rates were increased "significantly," but nobody seems to have performed (or published) an extensive enough analysis to pinpoint an honest number. One popular guesstimate puts the current discovery rate at 0.1% -- but really, your guess is as good as any. (Cauldron discovery rates are on a different table and run much higher than the general rate. Players report making cauldron discoveries, estimated at about 30%, as frequently as every one to five batches.)