Taking some close inspiration from already published sources can not only ease the creative endeavor from time to time, but also give your group a chance to change the course of fictional history. A few tricks are helpful along that route, though, or else your creative shortcut will likely lead to some dead-ends. Varying tastes from your players, ditching most details and leaving room for creative license are all avenues you should explore. Just remember that copyright infringement is a serious matter - do this for fun but never for profit.
The easiest issue with putting your players through circumstances that are already out in print or on the television is the fact that they might know the story you're drawing from, perhaps even better than you. That would be a lot like them reading the adventure module you just bought for their game. Along these lines, you might want to vary your tastes with theirs some. Zombie apocalypse scenarios, for instance, make up a massive genre - you aren't obligated to stick with the mainstream plots. Surprise them with some relative obscurity.
Leaving behind most details from the source is another way to protect your adventure from being found out prematurely. Skip this step if your players know of your plans but are willing to play along anyway. Unless that's the case, you're going to have to really blur things from the source to the session. Rare names, for example, should be replaced with one of your own choosing; people and places alike. It's all too easy to run an internet search for those and then wham, you've been found out.
Creative license wraps both of these paths together well. The less faithfully you stick to the story then the more room you have to engage in the role-playing game at the table. Force-fitting the player's actions into some predetermined plot is almost never a good idea, with the only exception being that your players consent to this type of railroading. Remember that your goal most likely isn't to recreate the borrowed story in detail - it's to take elements from it that you find enjoyable and reshape how it all transpires. Once your players enter the picture then it stops being under your exclusive control and becomes everyone's game. Happy borrowing!