Transform changes the user's current type, current stats, current stat modifications, current moves, current species, and current cry to that of the target's.
As of Generation 1, a transformed Pokémon copies the Target's current types, meaning it copies the effects of Soak, Forest's Curse, Trick-Or-Treat, Burn Up, Color Change, Protean, Libero, Conversion, and Conversion 2. :P
In the other answer, Showdown! wasn't as correct as it is today; in addition, the replay updated with Showdown! and shows the Ditto correctly turning into a Water type. :P
Hope I Helped!