Maybe your new years resolution didn't involve improving your recycling habits. Don't worry, I don't judge. Here's some info that may inspire you.
An Apple Core: One to two months or longer. Try composting it and adding it back to the ground when it's time to fertilize.
Paper: Two weeks to Five months. Just recycle it. All paper, even magazine paper is recyclable. Receipts, junk mail, newspaper, everything. Nowadays recycling paper is easy, just do it.
Cigarette Butts: 1-5 Years (another website says 12 years!). Just another reason to quit. They are made of cellulose acetate, and take forever to break down.
Aluminum Cans: 80-200 years. There are can recycling receptacles everywhere. If you don't have this service with your trash pick up, call them and ask why. If you haven't ordered recycling with your service, stop reading this and do it now.
Plastic Bottles: Unknown?! These don't break down, they break up. Into tiny little pieces that end up in the bodies of the animals we eat, which ends up into our bodies and it stays with us...forever. I would go out on a limb here and just say avoid using them period. Sure, if you have them, recycle them. If you can get your own reuseable water bottle and stop buying soda bottles you'd be doing everyone a favor. Use your power as a consumer and stop purchasing them. If no one buys them, they'll stop making them.
Plastic Bags: Unknown again. If exposed to air, they seem to be able to break down in 20-50 years, however air is in high priority in a landfill. Because of their inability to break down in a typical landfill setting many countries have begun to outlaw them. They are also one of the largest contributing pollutors to the Great Pacific Garbage Patch.
Glass: Unknown. It's estimated that a glass bottle could take upwards of a million years to decompose if it is not recycled. While it won't shred into tiny little pieces and end up in our food like plastic will, it's irresponsible to not recycle. Use glass, and use it again and again and again.
1. Landfill Trash
2. How long will my junk sit in a landfill?