Dubai's public transport system is probably the best in the Middle East, especially after the launch of the metro, but it's still a very car-oriented city and most visitors end up taking taxis quite often.

By metro

Dubai's 52km long Red Line, opened in September 2009, is the second metro in the Arab world after Cairo. While the line does not serve the old city center, it's handy for zipping along Dubai's long coastline and includes stops at the airport, Burj Khalifa and the Mall of the Emirates. The Green Line, which burrows through the city core, opened in September 2011. You can transfer between the two lines at Union Square and Khalid Bin Al Waleed (BurJuman). There are also Blue and Purple lines under construction with opening dates in the next few years.
Trains run every 3–5 minutes from 05:50 to midnight every day except Thursday and Friday, when services are extended to 05:50-01:00 limited to 13:00-23:59, respectively. All stations are air-conditioned and there's a large network of feeder buses. If you plan to travel late in the evening, check station working hours as the last train may depart earlier that the official system operating hours.

By monorail

Palm Jumeirah

Atlantis hotel

By tram

The latest of Dubai's modern transportation system is the Dubai Tram, which opened on November 12, 2014. It provides commuters a comfortable transit service around the prime business and leisure districts of Dubai. The Dubai Tram operates for 19 hours daily running for 14.5 kilometers along Al Sufouh Road. It passes around the vibrant Dubai Marina where passengers are treated to breathtaking sights of towering skyscrapers and luxury yachts and then travels down Jumeirah passing by the iconic Burj Al Arab.
The Dubai Tram connects with the Dubai Metro at the Jumeirah Lakes Towers and DAMAC stations, and links with the monorail of Palm Jumeirah. Outside of Europe, the Dubai Tram is the first tram system that uses the state-of-the-art ground cable system which eliminates the unsightly and dangerous overhead cables.

By bus

Dubai Public transport is a cheaper means of traveling within the several districts of Dubai. A map of the bus system can be found online, as well as detailed route maps and timetables. Public buses are clean and cheap, but unfortunately not very comprehensive and (on some routes) quite infrequent. The bus system is most useful for getting between different areas of central Dubai, or between the various suburbs, rather than general transport. Taxis or a fair amount of walking will also be required if you visit Dubai without a car of your own.
You will require a Nol card or ticket for fare payment. Cards can be purchased from most bus stations, metro stations, and sometimes from the bus driver.
The main bus stations are Gold Souq Market (in Deira) and Al Ghubaiba bus station (in Bur Dubai). Clear route maps and timetables are placed inside a few bus stands. Ramadan timings differ. The front seats are reserved for women.
Probably the single most useful service for the casual tourist is Line 8, which starts at the Gold Souq, takes the tunnel under the Creek to Heritage Village, and then sets off down Jumeirah Rd (just behind the beach) and all its hotels and malls, up to Burj al-Arab and Wild Wadi. It terminates near the Internet City, while its 8A variant goes down a little further and also serves the Mall of the Emirates.

By Hop-on Hop-off bus

For a good, hop-on/hop-off tour try Big Bus Tours. It runs two routes: the blue route through Jumeirah and the recently constructed areas, and the red route centered on the older parts of Dubai. The hub for both routes is Wafi City Mall.

By taxi

Taxis ply the streets of Dubai and are relatively easy to spot with their cream bodies and colored roofs. The easiest place to find them is at the taxi queue at one of the malls or outside a hotel. Waving down a taxi on the road is possible, but can be difficult during rush hours. At peak times (7-9 AM & 4-7 PM workdays, and Friday evenings) demand exceeds supply, and not only are taxis hard to find, but those who deign to pick you up may demand crazy off-meter fares or refuse short rides in congested areas entirely. If you accept an off-meter quote, ensure that the driver clearly says 'Dirhams' as occasionally the word metamorphoses into 'Dollars' when you reach your destination. Also, the drivers of Dubai Taxi Corporation go through their shift change between 4-6 PM daily and it can be more difficult to find taxis during this time. The standard of driving in Dubai ranges from poor to wild - taxis are some of the worst on the roads. Taxi drivers are pretty good at knowing where the main shopping malls and hotels are, however, less well-known places will mean the driver calling his brother-in-law to get directions, whilst he drives around in circles on your time - hence it is a good idea to have a rough idea of where you are heading or what a nearby landmark is.
The rates of all taxi companies — Dubai Transport, National, Cars, Metro, and Arabian — are identical, so just take the first one that comes along. Taxis are exempt from the Salik road toll charges.
Beware of unmarked hotel taxis and limousines though: while some of these are metered, they are not tied to the official rates and can be much more expensive. One way to spot whether a taxi is official or not is to look for a meter: no meter, don't get in.
If you can't find one otherwise, you can attempt to call Dubai Taxi on 04-2080808 (each franchise has its own booking number but one central system). The booking system was notorious for its unreliability but with a significantly increased taxi fleet, many taxis now deliberately wait in unofficial holding areas waiting for bookings. As a result, on a good day, it can be possible to book a taxi and have it arrive within less than five minutes.
Women should travel in the back of the taxi as some drivers see it as a sexual invitation if you get in the front.
Taxi drivers are usually friendly but may have different ideas on hygiene.

By car

There are a countless number of Rent-A-Cars that will provide a mode of transportation for very cheap rates and very little paperwork. An International Driving Permit is not necessarily required, but hire companies may not rent a car without one.
Some agencies will hire out cars complete with drivers. Visitors taking advantage of this option will need to make certain that their driver knows his way around as many do not.
When driving on the main roads, such as Sheikh Zayed road, the junction numbers are not in logical order. Junction 13 is just after Junction 18 and are rarely as shown on the maps. Road names can also be very confusing with slight differences in spelling (due to different transliterations from Arabic) being very important. The construction work that is taking place throughout and around Dubai can make finding your destination a challenge. Temporary road layouts change with alarming regularity and temporary signs can be misleading or nonexistent. As GPS maps are not up to date (and usually not anyway available to rent with hire cars), you will be very well off with a printed map (you can get an excellent one in Virgin stores, for example. There is a Virgin Megastore on the top floor of City Center).
Driving during morning and afternoon peak hours is not recommended, as traffic slows to a standstill and even a simple trip across a bridge can take up to 45 minutes. There is also a scarcity of parking spaces in many parts of the city.
With such a mixture of nationalities residing in the city, driving styles are mixed, to say the least. Both dangerous and experienced driving will be witnessed or experienced frequently, and bear in mind that Dubai has one of the highest per capita road death rates in the world. There is zero tolerance for alcohol and driving with stiff penalties meted out including jail and deportation.

By boat

An easy way of crossing Dubai Creek is by abra, a small ferry. Abra stations are located along the Creek on both the Bur Dubai and Deira sides, and the system of filling the boats is remarkably efficient. The cross-river trip costs 1 dirham, payable to the driver after the boat has left the station, and affords a very picturesque view of the city. Abras set off very regularly, and the service is available round-the-clock.
Air-conditioned water buses are a way to avoid the abra crowd and the heat. They are part of the public transport system, so a Red Nol ticket or a Nol card is required. Tickets can be purchased at the water bus station. The water bus also features a 'tourist route' round trip – while it is convenient, it can get quite expensive).
The Creek is also the home of many boats offering more comfortable (and correspondingly more expensive) tours, often in boats designed to resemble dhows. Prices tend to be higher, particularly for dinner cruises with onboard entertainment.