There are lots of reasons that you may have a bottle that you haven't touched in while. Maybe you're a whiskey collector at home, or you've come off a dry period, or you've happened to come across a bottle in a liquor store or estate sale. When I open an old bottle of whiskey, I'm always preparing for cork failure. I always flip the bottle over to get the cork a little wet. Then I twist the stopper slowly before starting to pull it upward, while constantly rotating it.
Still sometimes, the topper will pop off of the cork, or the glue will give way.
That's when I use a cork popper. If you don't have one of those, a regular old cork screw can do the job if you don't have a lot of crumbling. Worst case, I know many of you have been there--use the good old butter knife, and push that cork down into the bottle!
Good bottle maintenance will help you avoid cork failures. Nevertheless I encourage you to save your old corks and stoppers. Where some people have a packet drawer where you keep to-go order ketchup, soy sauce, duck sauce, or whatever, I use it to store my old corks. True, you can dump natural and synthetic corks into the recycle bin, But the best usage is on a bottle that's got a busted cork!