A lot of writers are messing up these two words, though for the most part, it appears to be done inadvertently.

Accidently seems to be right, as accident is just being used as an adverb, which means adding ly, as in He accidently knocked over the vase.

Alas, accidentally is the correct spelling. To get an adverb, rather than tack ly onto the end of a noun generally we add it to an adjective or a verb. In this case, accidental – an adjective – is the word we use to get to the adverb. The correct version of the above example sentence would be He accidentally knocked over the vase.

Of course, as accidently becomes more widely used, dictionaries increasingly are listing it as an acceptable alternate spelling. Until the spelling becomes universal, though, stick with accidentally.