Arabic is the official language for both written and verbal communication in Dubai. Government offices and affairs are conducted in Arabic, and rules and laws are published in Arabic.
Arabic is mainly spoken by the natives of the UAE, called Emiratis. You can get by with just speaking English in Dubai, but if you are ready to learn Arabic you will probably be more welcomed by the Emiratis.
English is the most widely spoken language in Dubai, especially for business, trade and tourism. Around 75% of the population in Dubai are expatriates, most of whom speak English or their native language. There are a lot of different nationals working in Dubai, so you are likely to find someone who speaks your language.
If you can speak a South Asian language (e.g. Hindi, Urdu, Malayalam, Bengali and Tamil), you will have the opportunity to practice in Dubai. Many expatriates are from South Asia and some of them only speak their native language.
The problem of the growing number of English speakers has been raised during discussions for the Dubai Strategic Plan for 2015. It is a project for Dubai's development proposed by the UAE Prime Minister and Vice President. The government is afraid that the UAE is losing its national identity.