Taxis in Amsterdam
Taxis do not generally drive all over the city constantly to pick up fares as in other European cities, although independent taxis depend more on street fare pickups so this is changing.
You can phone for a (TCA) taxi on (020) 777 7777, or go to a taxi rank (an area marked off on a street where the taxis will wait for their fares). Often there are also taxis waiting near the larger hotels. At a taxi rank you DO NOT have to take the first taxi waiting - by law you have a free choice to choose the one you prefer (more attractive driver, non-smoking/smoking, cleaner, TCA/non-TCA - whatever reason you have is OK - although you can expect some less professional drivers to complain if you don't pick them).
There are different types of taxi in the city - most people will recommend a TCA taxi (or another company-linked taxi) over an independent taxi. Although there should be no difference in fare - the TCA drivers are more likely to really know their way around, speak good English and Dutch and, if you loose something or have a problem, there's a central phone number to call (020) 677 7777 to sort it out (just take the taxi driver's number).
From Amsterdam to Schiphol it is better to book a taxi in advance. There are numerous taxi services that offer attractive fixed price transfers. Most hotels will also have arrangements with taxi companies to offer fixed-fare transport to the airport. Expect to pay around 40 to 50 euro for a trip from the city center.
With the independent taxis that's not the case. Most are reputable, but perhaps 25% aren't. There are locations in the city where you'll find it difficult to get a TCA taxi - notably Central Station and Leidseplein - where there are long rows of independent taxis that have been known to show problems (refusing short trips, wanting to ride with the meter off (never let that happen!), refusing a blind passenger with a guide dog...) Taxis in Amsterdam are pretty expensive so it is recommended to only give a small tip, if at all - really it is a bonus for a good, friendly driver, not just something that has to be given.
At Central Station, the best advice is try to know where you are going and don't go off the meter. At Leidseplein, never use a taxi in the line. Just hail one right there who hasn't been waiting an hour in line with dreams of taking you to Rotterdam instead of to your nearby hotel.
Overall, Amsterdam is such a compact city with other good public transport (and bikes!) you may not even need a taxi! The train is considered by many to be the best way to get to and from the airport and the city center (for example if you are staying anywhere on the Damrak or streets nearby - such as Swiss Hotel, Crowne Plaza, Renaissance Hotel - these are all easy walking distance from the station if your suitcase has wheels!).
Before you go, you can use this website to calculate the taxi price from point to point (Amsterdam area only) http://www.worldtaximeter.com/amsterdam
Car rental
(moved from "Rent a car" topic. Work in progress)
All major car rental companies are represented in Amsterdam. Schiphol airport has offices of Sixt, Avis, Europcar, Hertz, Budget and National. These have offices in the main plaza (all 06:00 to 23:00), and store their cars in the large garage opposite the plaza.
Airport pick-up is a few euros per day more expensive than pickup in the city. When staying for a longer time, it is generally cheaper to first take a train to the center and pick up your car there.