Many of the products we use day in and day out are not biodegradable (meaning they will not safely eliminate themselves over time), so they take up valuable landfill space or must be incinerated, both of which are bad for the environment. Recycling creates a safer alternative, allowing some of these products to be reused for the same or similar purposes. Glass, plastic, and aluminum have almost limitless lifespan and can be used multiple times without ever losing quality. Paper, on the other hand, can be recycled, but it will lose some of its usefulness. The reason for this is that as fibers are recycled, they are shortened, causing them to not be as useful in higher quality products. Paper should certainly still be recycled, though.
Another possible incentive for recycling, albeit a greedier one, is financial gain. Many states (California, Oregon, Hawaii, Connecticut, Vermont, Delaware, Maine, Massachusetts, Michigan, New York and Iowa) offer a small refund on beverage containers (both bottles and cans) to give people more incentive to recycle. The refund in Michigan is ten cents per container, while it is five cents in all the other states. Many have had grand plans of taking a trip to Michigan with a vehicle full of bottles and cans to get the lucrative ten cent deposit, including the characters Kramer and Newman in the renowned television show Seinfeld. In a two part episode entitled "The Bottle Deposit," the two quirky characters use one of Newman's mail trucks to make the journey, which of course is foiled by numerous mishaps along the way. With gas prices today hovering around three dollars per gallon, it would be difficult to imagine anyone who doesn't live in Michigan having a good enough reason to take their recycling there.
A variation of recycling is simply called reuse. In recycling, the good material is reduced to raw material to make a new good material (for example, the glass bottle is crushed up and made into new glass). In reuse, the bottle would simply be refilled. (Don't worry, there is an intense method of proper cleaning in place anywhere bottles are refilled and reused.) This method of recycling is especially popular in many European countries, where as many as 98% of bottles are refillable.