Why were cigarettes called fags? Are they still?

Could be!

My dictionary defines fag as weary, from hard and unpleasant work, or the work itself; and also cites the tradition in old-time English public-schools (British definition of "public school") of "fagging" - menial duties carried out for senior boys by juniors co-opted as "fags" for that purpose.

It also gives fag as slang for cigarette; which itself is a French form of the Spanish cigarillo ("small cigar"). That was originally a cheap, rough-and-ready way of smoking by the destitute or 16C Spain, using discarded cigar-butts; but the principle of shredded tobacco in a paper tube became an habit across Europe for those who could afford commercially-made but still hand-rolled, smoking-sticks. Cigarettes became much cheaper only in the late 19C with the invention of machine-rolling.

Still no sign of the word "fag" though, and my dictionary tells us the etymology is uncertain. 

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So I looked up faggot, too, finding it is from an old French word, fagot, meaning simply a bundle of sticks. Nothing obviously to do with cigarettes.

I don't know if fag for cigarette is common the America, but it is still common in Britain. A result of the law banning smoking indoors in work-places, is the phrase "[just nipping out for a ] fag-break".

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One curiosity I found in trying to learn the etymology of a slang word, is the trans-Atlantic exchange of tobaccos. British smokers' tastes favoured Virginian tobacco whilst Americans went for blends with Turkish tobacco! It made me think of the saying "ships passing in the night" - two vessels exchanging greetings somewhere South of the Denmark Straits while each carrying container-loads of tobacco in opposite directions.

:):):)

Huh. I wonder why over time that word was applied to homo saps? Though we do call homo saps dogs or rats or chickens don't we? Strange how words begin as one thing and end up as quite another isn't it? Thank you for your reply Walt and Happy Saturday! :)