Most Muslims want to be able to read the Qur'an in Arabic. Many mosques offer lessons in this field as do select universities in the U.S. and abroad. Such courses usually focus on the classical aspects of the language, paying special attention to correct pronunciation, grammatical structure and acquisition of Qur'anic vocabulary which may otherwise be out-dated by MSA standards. Good courses also help the student to understand the intricacies and the historical backround of the Qur'anic Revelation.
Most Muslims would also like to be able to communicate with Arabic-speaking brothers and sisters. In such circumstances, Classical Arabic is not a sufficient means of modern-day communication. Though it is undoubtedly the most beautiful, special language in the world, the fact is that people just don't walk around speaking Classical Arabic. Doing so would be the equivalent of 21st century Americans chit-chatting in Shakespearean English.
MSA is a good alternative to Classical Arabic. Somebody who studies MSA formally can expect to get a good overview of the Arabic language as it is used in well-educated circles. He will also learn to read and write. These basic skills make an excellent jumping off point to go on to study either Classical Arabic or one of the many Arabic dialects.
However, like Classical Arabic, MSA is still a little lofty for everyday conversation. Arabs who are familiar with MSA as the result of television exposure but who have not formally studied the language may understand you when you speak but only be able to answer you in their own dialects. Regardless, MSA is still the language which will allow you to communicate with the greatest number of people from all over the Arabic-speaking world.