Shadowdancer is the only class I can think of. Rangers and Scouts get an (Ex) version at higher levels, but that is much less useful.
Shadar-Kai (Fiend Folio) is a playable race that also gets this (along with a huge racial skill bonus to Hide checks), and an even better bet might be the cheaper Dark template (Tome of Magic).
Another way to get the same effect might be spells, class abilities or magic items to make you invisible, especially if it can be done quicker than a standard action. Swift Invisibility would be the obvious spell solution.
Another interesting idea would be a Shadow Hand focused Swordsage (Tome of Battle)/Rogue with the Gloom Razor feat and the Child of Shadows stance.
(Still another would be plain Ninja [Complete Adventurer] for Ghost Step, but I don't really endorse the Ninja class, as it is rather less useful than good old Rogue)