After mankind figured out workable agriculture to replace its hunting and gathering gustatory modality, the next step was figuring out how to preserve that food for travel or spare times. Different cultures found different ways of doing this, most of them learning to dry vegetables and grains for storage, and preserve meat in salt where available. Being able to pack provisions and trust that they would last for at least a few weeks is one of the big steps that enabled our six-continent diaspora.
Times haven't changed that much. Modern fresh food, surprise surprise, will also not remain edible very long if left unpreserved -- a matter of days at best. Microbial organisms like molds and bacteria attack the food, leaching nutrients from it and leaving poisonous byproducts behind. Also, oxygen may react with chemicals in the food's oil content, changing their structure and making the food itself discolored, rancid, or otherwise icky. With these two problems come two classes of solution, antimicrobial and antioxidant treatments, respectively. Which isn't to say the old methods aren't still used, check the Quaker Oats in your kitchen or the beef jerky at the corner store.
Antimicrobials
Sodium benzoate is a water soluble preservative, and is used mostly in fruit products like jams, fillings, etc. It is suited for these applications because it is most effective in foods with a pH between 2.5 and 4.0, that is, foods which are relatively acidic. While it has tested safe even at high concentrations (the FDA limit is .1 percent), it is used at much lower levels so as not to distort the food's flavor. Potassium sorbate has more-or-less the same statistics, though it is effective in pH of up to 6.5, allowing its use in dairy products, canned fruits, and many other foods.
Propionates are effective against molds and some bacteria, but do not disturb the metabolism of yeast. This makes them perfect for preservation of bread, both during its manufacture and storage, though they are counter-indicated (i.e. they will stop the process) for non-yeast leavening. Propionates are completely safe, and in fact propionic acid is generated during the fermentation of some cheeses. This is one of the reasons cheese may be able to last a long time in storage, the propionate content may account for up to 1 percent (!) of some types' final weight.
Parabens are most effective against yeasts and molds, and are often used for their versatility over temperature and pH ranges. Actually, they dissolve best in water just below boiling temperature, and can function in pH ranging between 3 and 8. Versatility here comes at a price, as they are more costly than other preservatives and tend to noticeably distort the flavor of food. FDA regulations allow a maximum concentration of .1 percent by weight.
Antioxidants
BHT and BHA, butylated hydroxytoluene and butylated hydroxyanisol, are two common antioxidant preservatives. They are limited by the FDA to .02 percent of a food's fat/oil content, and have set parts per million levels for foods without appreciable fat content. Research has shown these additives to be carcinogenic at high levels, though at recommended levels they are given "generally recognized as safe" consideration by the FDA. Animal studies have been done which give above the recommended dosage over long periods of time, up to five years, with zero increase in cancer rate.
Sulfites are another class of antioxidants, which are generally used on fruit and vegetables to prevent discoloration, and also in wine as they are antibacterial but allow yeast growth. Some people are sensitive to sulfites, and can have (almost always nonlethal) adverse reactions to them. Because of this, FDA regulations say that foods must warn about sulfites on the label if foods have more than 10 parts per million of the chemicals. Also, food being sold at salad bars or other fresh-food avenues may not be sprayed or exposed to sulfites to preserve its color. However, cooked food such as French fries often is bathed in the chemicals beforehand, so sulfite sensitive people are advised to be careful.