Sedan taxis at the airport have now raised their base fare to 20dhs + km charges while regular sedan taxis OUTSIDE the airport have a base fare of 3 or 3.50dhs plus per km charges. I’ve taken plenty of short taxi rides in town for a total fare of less than 10dhs (around 2 euro). If the distance is less than 2 km in good traffic, the fare is usually around 5dhs (1 euro)… so don’t get too caught up in taking public transportation unless it’s for longer distances; especially if there are a few of you.
There is a red light shining on the taxi sign if engaged (has passenger already). For fares I really didn’t notice much of a difference between the dozen+ different companies operating in Dubai, so I would not say to specifically ‘avoid’ any company. The fares were all fairly comparable for similar distances in good traffic in the very common Toyota sedan taxis. Waiting times in traffic can drive up prices considerably.
I also learned that taxis are exempted from Salik fees (toll system on Dubai’s roads), so you should not have anything added to your fare for ‘tolls’. Being ripped off by taxis drivers in Dubai is rare.
The minimum nighttime fare in Dubai is 10dhs, so the final fare will automatically adjust up if lower; that is around 5km in good traffic. If your total fare is higher than 10dhs, then the fare will be the same as in the daytime.
There are family taxis, women's taxis, regular sedan taxis, special needs taxis and luxury taxis. An informative page on most of the different types of taxis and their fares can be found here.
I should also mention non-licensed ‘taxis’ which are simply people trying to make some extra cash by driving people around in their personal cars. These will loiter around shopping areas and even near crowded bus stops to offer a lift. While taking an 'unofficial taxi' is technically illegal, it’s a fairly common practice here; especially for lower paid workers looking to save on transportation costs. Most people offering these services are from India, Pakistan or other Arab countries. The UAE is a fairly safe country by international standards, but there is always some risk getting into a total strangers vehicle. It will definitely be an adventure with some these drivers reportedly going up to 160km per hour trying to get you there quickly!
Tip: If taking a taxi you can ask for a receipt for itemized travel expenses and if you forgot anything in the taxi, the receipt will include the taxi vehicle number, driver name and company phone number.