The savoury, mouth-filling taste known as umami occurs naturally in some foods, such as oysters and tomatoes. It turns out when you pair certain complimentary ingredients, you can amplify the savouriness by thirtyfold. Cook's Illustrated explains the science behind magnifying umami.
Picture: Umami Information Center
In its May/June 2012 issue (subscription required), Cook's Illustrated says that when you combine ingredients that are naturally rich in glutamates with ones rich in nucleotides (guanylate or inosinate), the umami flavour of a dish is dramatically amplified. They did an experiment comparing MSG in water with a solution of inosinate/glutamate powder and found that tasters found the MSG only "moderately" or "mildly" savoury, but the umami boosters got a perfect score for savouriness.
Not a big fan of chemistry? Don't worry, all you need to know is that some ingredient combinations naturally are more flavourful. Foods rich in glutamate include: parmesan cheese, fish sauce, soy sauce, tomato paste, cured ham, anchovies/sardines, beef, cheddar cheese, and Worcestershire sauce. Pair them with these foods rich in nucleotides: anchovies/sardines, dried shiitake mushrooms, pork, beef, dried porcini mushrooms.
You'll notice that some ingredients are rich in both, so you can add them to any dish to amplify the savouriness. (Also, no wonder cheeseburgers taste so good!)
For further reading, the Umami Information Center has much more on the science and history of umami, as well as recipes. You could also get a free 14-day trial to Cook's Illustrated online to read the article mentioned here.
Amping Up Savoriness in Food [Cook's Illustrated]