I know I can not smoke on a airplane but can I pack cigarettes in my bag so I don't have to buy them when I get to my destination?

Normally yes, but you want to check prior to travel what is the allowance permitted when entering the country you are visiting. For instance in Europe most of the countries allow 200 cigarettes (10 packs of 20 cigarettes) but in Singapore you are only allowed 40 cigarettes (2 packs of 20 cigarettes).