My boys do not have strong vocabulary, largely due to insufficent reading. However, vocabulary is an important skill in the USA. It is used to measure how smart a person is, in tests and in real life. This explains why vocabulary has a significant part in SAT and GRE.
The best way to increase vocabulary is through reading. Books, the Time magazine and the New York Times are good sources. To prepare for tests, I found that the vocabulary builder in the number2.com a wonderful tool. It shows you new words in the form of a multiple-choice question. It keeps track of words that you have answered correctly once, twice and never. It helps you to memorize words that you have difficulties with. My younger son just started the vocabulary builer. He will take SAT in January 2006. We will see how it goes.