Taxis

Get information on local taxi regulation: Each country and city has different regulations and payment schemes for taxi travel.
Have the destination address written down in the local language: Drivers might not be fluent in your language.
Follow local customs for tipping: While tipping is expected in some places (most low-income countries as well as the USA), it can be refused in other parts of the world (such as Japan).
Be aware of traffic conditions: During rush hour and special events, taxi travel might be a worse choice than urban rail.
Be aware of taxi scams:

If possible have a rough idea of where you are going and the fastest way to get there. Dishonest taxi drivers sometimes make unnecessary detours in order to charge higher prices.

If there is no meter in your taxi or meters aren't used in your destination-country agree on a fare before entering the cab, as once you are in the cab your bargaining power is severely limited if not gone entirely.

In places where haggling is common and taxis don't use meters expect to bargain for a fare.

Make sure in advance that you have proper money to pay the ride. Some, but not all, cabs take credit cards. Some cannot change large banknotes.

"Unlicensed taxis" are usually a bad idea as the small amounts of money they might save you are not worth the (sometimes significant) risk of theft, or abduction amongst other risks. Another reason for avoiding unlicensed taxis is that the driver and operator aren't necessarily subject to the safety checks (of both driver and vehicle) that a licensed one would be. If a taxi-driver doesn't have a license, they can't lose it as a punishment for bad behavior, thereby a taxi license discourages criminal, unethical or unsafe practices to some extent.

Avoid taking taxis parked outside tourist attractions or hotels, as these taxi drivers are likely to be waiting to scam unsuspecting tourists. Instead, flag down a taxi that is cruising down the street, find a taxi stand that is used by the locals, or use a ride-hailing app, as you are more likely to get an honest driver this way.

Find out what the major reputable taxi companies your destination city are if they exist, and stick only to taxis operated by those companies, as the risk of scams is far lower.

When arriving at a major airport and there is no public transit option you'd consider viable, avoid touts in the arrival hall and only use the official taxi stand.

A cycle taxi, or a rickshaw, is a three-wheeled bicycle for hire, especially common in Asia.

A motorcycle taxi, also known as an auto rickshaw, baby taxi or tuk-tuk is a three-wheeled motorcycle for passenger transport. It is common in large cities, especially in Asia. Also plain motorcycles, mopeds or bikes are used at some destinations, such as the boda-bodas of East Africa.
For examples, see Thailand#Tuk-tuk or Philippines#By_tricycle.

If you are staying in a place with good mass transit (urban rail or buses) using it might often work out to be not only cheaper but faster as well.
Many city-centers are entirely walkable and if you aren't mobility impaired a two or three kilometer stroll is entirely doable. Also walking is a great way to get to know a place and you can simply enter any interesting shops, restaurants or museum you might pass without the driver having to look for (often scarce) inner-city parking space.
In more and more places, cycling is the best way to go short to medium distances and several cities around the world have implemented bike-sharing programs that are a great alternative for visitors as well as locals. Bikes are available for rent in many more places.
Ride hailing services such as Uber, Haxi and Lyft offer taxi-like service using private vehicles in many cities. Ridesharing and hitchhiking may also be alternatives.
Taxis are most frequently used for getting to and from airports. Look around, if there really is no public connection or shuttle service of any kind, you may ask whether your hotel offers pick up and drop off service. This is sometimes free to encourage you to stay at their hotel and more often than not cheaper than a taxi. In Europe and increasingly East Asia a major airport without a rail or urban rail connection is a rare sight indeed. Even notorious no frills airports like Hahn nowadays at least have a bus connection (sometimes bookable through the airline website, although there may be cheaper ways)
If you are staying in a place for a longer time or plan to go on a road-trip anyway consider renting a car, with or without a driver. Carsharing services are an alternative provider for short term self-serve hire car rentals.

Taxis

Hints for riding a taxi

Cycle taxis

Motorcycle taxis

Alternatives