Different Cuban Taxis
There are some taxi companies like Panataxi and CubaTaxi. There is also the Cuban vintage taxi called the "Almendrón", very popular among the Havana´s people. The Coconut-Taxi (taxi with the shape of a coconut) is a popular option for tourists, as well as the Bicycle-Taxi (kind of bycicle) for short distances.
Panataxi and CubaTaxi are expensive, usually the minimum price for any distance is 5 CUC, commonly the taxi driver wants 10 CUC or more. The travel from the airport to Havana city costs between 35 CUC and 40 CUC with this kind of taxi. It is a good idea to coordinate with the house rental website for having a car waiting for you at the airport, the price usually is only 25 CUC and it is more sure, because some taxi drivers of Panataxi and CubaTaxi at the airport take the tourists to a different rental house looking for money from the owner of this new house.
For going to different places in Havana it is a good option to take one of the "Almendrón" taxis, they are collective cars with fixed routes and the price always is 10 Pesos Cubanos (approximately 0.40 CUC), no matter if you are a tourist, the price is the same for tourists and Cubans. Many tourists dont know this and they pay 10 CUC. It is a big mistake, this way you are paying 240 Pesos Cubanos!