Cigarette butt : 18 months - 10 years
Cigarette Butts are made of plastic, of the same type of plastic as is found in plastic bags and soda bottles. They will eventually degrade, especially if the environment is right for that sort of thing (moist, warm, and shady) but they will take much longer to degrade if flicked away on a beach or some other sandy, dry, hot area. The nicotine contained in 200 leftover cigarette butts, however, is enough to kill a full-sized human being (according to the admittedly biased http://www.whyquit.com/), and can have a negative impact on the wildlife in the area.
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"[Cigarette butts] also present a threat to wildlife. Cigarette filters have been found in the stomachs of fish, birds, whales and other marine creatures who mistake them for food … Composed of cellulose acetate, a form of plastic, cigarette butts can persist in the environment as long as other forms of plastic."
5 years! :((
http://www.thegreenestdollar.com/2009/05/how-long-our-garbage-lasts/
A cigarette takes 3-10 months to mostly decompose and some say it can take up to as much as twelve years; however, the filter which is made of acetate will NEVER fully break down.
I don't know about a whole pack of cigarettes but it takes five years for one cigarette to break down naturally. So i guess you could times that by the amount of cigarettes in the pack.