I've been experimenting with growing grain in my suburban backyard. It's fun to think of growing grain and then converting it to beer. In this posting, I provide information about the ingredients in beer and the four reasons why growing your own ingredients isn't practical.
Basic Beer Brewing
Beer is made from just four basic ingredients: water, yeast, barley and hops. The later two ingredients can be grown by gardeners and this raises the tantalizing possibility of not only brewing ones own beer, but doing so from home grown ingredients. Let's look in greater detail at barley and hops....
Hops
In beer production hops are used as a preservative and a flavoring agent, giving beer its classic bitter taste and aroma. The female flower cluster of the plant humulus lupulus (hops) is harvested and dried. These flowers are then added to the beer during the brewing process where they release alpha and beta acids. The alpha acids give beer it's bitter flavor, while the beta acids add aroma.
As a plant, hops are a perennial vine that grow 12-15 feet high. They are extremely cold hardy and can be successfully grown in zone 3 through 8. Hops are fast growers and will wrap themselves around trees, telephone poles and anything else in your garden. So successful are hops that many consider the plant to be invasive. Hops seeds and rhizomes can be purchased from both seed companies such as Jungs Seeds, Raintree Nursery and a number of stores that cater to home-brewers. 
I've never grow hops, but fellow gardeners and home brewers who have, often report that while easy to grow, hops are not easy to grow in a way that makes their alpha and beta acids consistent from plant-to-plant or year-to-year. Herein lies the first problem.
Reason #1 - To make good beer, home brewer needs hops that are consistent with regard to their alpha and beta acid levels. This is hard to achieve in a home garden.
I've been referring to hops as if there were only one type of this plant in the world. The truth is that there are dozens of varieties and each of these differs dramatically in their bitterness and in the aroma that they impart to the beer. (See the Wikipedia for a list of some common varieties) This highlights the second issue for those interested in growing hops for home brewing...
Reason #2 - Most beer recipes require two or more different varieties of hops. If you want to drink several types of beers, this means a home grower will need to successfully and consistently grow many hops varieties. For example, a recipe that simulate Sam Adams Boston Lager requires the addition of Hallertauer and Pearle hops. A recipe that I have for Bear Republic Racer #5, a craft brew, calls for five different types of hops - Chinook, Cascade, Centennial, Columbus and Amarillo.
Barley:
The second major ingredient in beer is barley. Barley provides the sugars that are fermented by yeast into alcohol. As grain, barley does not possess these sugars and the grain needs to first be malted for use in beer. In this process, the barley seed is soaked in water so that it begins to germinate and starches within the grain are thereby converted to ferment-able sugar. Germination is then suspended by air drying so the barley can be used by brewers. In some cases, the grain is then further processed by roasting. This malting and roasting the grain contributes importantly to the final color, taste and mouth-feel of the beer. The longer the grain is roasted, the darker it's color and the stronger it's flavor. For example, home-brew versions of Guinness Stout use British Crystal Malt (provides a reddish color and carmel sweetness to the beer), Black Patent Malt (has a very sharp flavor and is used to make Porter and Stout style beers) as well as English Pale Malt and in some recipes wheat. 
It's certainly possible for gardeners to grow barley. The issue is really that that beer recipes generally require more than one variety and more than one malting style.
To begin with, there are three major categories of barley based on the number of seeds at the top of the stalk (two-row, four-row and six-row barley). Two and six row barley are the ones that are most frequently used in brewing. They differ in the amount of protein they contain and therefore in the taste and mouth-feel of the beers they produce. European beers are generally made with 2-row barley while American brewers tend to use six-row. Within these broad groups, there are many different varieties and these differ in their flavor characteristics as well as the ease of which they can be germinated for malting. Most professional malting companies will use several varieties of barley to try to keep their products uniform. These grain and malting variations form a highly complex palette from which a brewer can choose to formulate a beer recipe.
Reason #3 - As with hops, if you want to grow your own barley for brewing you'll probably need to grow several varieties, not just one.
Reason #4 - These grains need to be malted (a complex enough process to begin with) and most beer recipes require between 2 and eight types of malted grain; malting this many styles is probably beyond the scope of what any home gardener/brewer has the capability and time to do. For perspective, Austin Homebrew, is a company that sells malt grains to home-brewerssells over 56 different varieties of malted grains on their web site.
The Bottom Line
There's a difference between creating a beverage that would be recognized as beer and one that would be enjoyable and worth the effort. You can grow one type of barley and roast it, and one type of hops and dry it. From these ingredients it is possible to create beer.
However, to make a beer that would be as good as commercially available beer, you'll need several varieties of malt (barley) and hops. This is very really just beyond the scope of what can be produced from the home garden and processed at home.
