I've rarely played games in which characters have enough downtime, enough resources and enough skill to concoct alchemical potions. However, PCs have often taken the Alchemy skill and used it to: identify potions, analyze newfound substances, identify/subvert the plans of alchemist villains, etc. It ends up functioning as a kind of "Hidden Lore" for potions, elixirs, and so on.
DF2 includes rules for how Alchemy can be used to determine the general properties of a magic item.
Jason "Reverend Pee Kitty" Levine has some great house rules for Alchemy in DF
here. I've never tried them, but they seem awesome.