What is a good definition of beer?

The definition of beer lies in the -process- used to make it. Beer is a fermented alcoholic beverage created by mashing grains to convert the starches contained within to fermentable sugars. Technically Sake is a type of beer, not wine, as it mashes grains (rice) to convert the starches to fermentable sugars and is then fermented to an alcoholic beverage. Associating Sake with wine is simply a good marketing move.

Wine is wine, no grains are mashed, the sugars are provided by grapes without requiring a conversion to fermentable sugars.Mead uses Honey to provide the sugars instead of fruit or mashed grains. Cider uses apples, typically, but sometimes other closely related fruits such as pears. Then there's flat out crazy stuff like Braggot to confuse the issue even more.

I like Dustin's definition. The German "law" is unnecessarily restrictive in my opinion.

If we talk about "lager" or "ale" we can get more specific (a beer that has been lagered, or a beer based upon malted barley and warm-fermented), but for beer I'd go with

So, mainly, beer is a fermented beverage based on grain.

I have just started reading a book, 'Brewing' by Dr Ian S Hornsey (Published by the Royal Society of Chemistry). Aside from being a lecturer in Botany and Microbiology, he is a practising brewer. The opening chapter is called "The definition of Brewing". Not quite what the question asks but I thought this was worth an answer. The chapter begins:

"In the broadest sense of the word 'brewing' may be defined as 'The combined processes preparing beverages from the infusion of sound grains that have undergone sprouting, and the subsequent fermentation of the sugary solution produced, by yeast - whereby a proportion of the carbohydrate is converted to ethanol and carbon dioxide.'"

He goes on to say...

The modern connotation of the word would imply 'production of beer', in all its various forms - and this is how the author has interpreted it.

It seems to cover all bases.

The definition of beer is a fairly wide one. I'll quote from wikipedia:

[Beer] is produced by the brewing and fermentation of starches, mainly derived from cereal grains—most commonly malted barley, although wheat, maize (corn), and rice are widely used. Most beer is flavoured with hops, which add bitterness and act as a natural preservative, though other flavourings such as herbs or fruit may occasionally be included.

So, mainly, beer is a fermented beverage based on grain. Hops are optional, and, in fact, there is no record of their use in beers brewed before 822. Again, from wikipedia:

What they did not contain was hops, as that was a later addition first mentioned in Europe around 822 by a Carolingian Abbot[24] and again in 1067 by Abbess Hildegard of Bingen.

Hope this helps!

Beer is malted grain, hops, water and yeast at is most basic. Category 15 used malted wheat or rye... that's german Reinheitsgebot friendly. Otherwise it wouldn't be GERMAN Wheat and Rye Beer.