Covered in this page are ways of travelling that are not public transport (i.e. you do not have to share the vehicle with unknown passengers), but also not do-it-yourself options. (For airborne options, see the sky page).
There are plenty of taxis in the Netherlands. Many line up at the usual places that you would expect them: airports, larger train stations, night-life areas. You can also ring taxi companies to make a booking, and some also have online/app booking options. All taxis have metres, and you should receive a receipt at the end of your trip. See what the government says, and what the tourism board says about taxis and taking taxis in the Netherlands. Here is a list of all(?) taxi companies in European Netherlands. With watkosteentaxi.nl, you can type in the beginning and end points of your intended journey, and it tells you roughly how much it cost to take a taxi for that distance (congestion surcharge and road toll not included).
NS Zonetaxi (or this page for people with a NS-buisness card) is a cheap taxi option. You have to have an account with them first. You can book an NS Zonetaxi to/from more than 130 train stations in the Netherlands, and NS Zonetaxis operate during times that a train connection can be made. The maximum distance they can travel is 30km from a train station, on a route based on their route planner.
Some companies cater for customers with specific mobility needs. Another option popular with people with difficulties accessing regular public transport is regiotaxi (see the page on regiotaxi's).
UberPop has been ruled illegal in the Netherlands (and also in Belgium, France, Germany), and is actively cracked down on by the government. Other Uber services are available in Amsterdam and Rotterdam (September 2016). There are also other similar local start-ups. See, e.g. Remco Janssen's reply to this question, and also his blog (most posts are in Dutch, but some are in English).
In the unlikely case that a klacht 'complain' needs to be made, try contacting the taxi company, or try taxiklacht.nl, or contact the Politie in the Netherlands for more serious matters. (Politie in Caribbean Netherlands.)
Carpooling is popular in the Netherlands, for both domestic and international trips. The biggest company is BlaBlaCar. You type in your inteded origin and destination, e.g. from Rotterdam to Brussels, from Istanbul to Amsterdam. You will then see a list of (private) drivers who are going on the same or similar trajectory, if there is a match. It also tells you how much that journey costs per seat, and how many empty seats are left. You can narrow down the search results by factors like time and date, and 'expertise level' of the driver. You contact the driver through the website, (the driver could potentially give you other contact details like e-mail, phone number, WhatsApp) and you can make further arrangements with the driver about details like where to pick you up and where to drop you off, how much detour they are willing to make, how much luggage they can take, etc.
From the other side of this interaction, as a driver, you can post on BlaBlaCar the route that you will drive, time, date, and other details, and BlaBlaCar will give you an advisory range of price that you can charge each passenger. The aim is just to share the cost, and not to make money. Do not expect to make a profit (but you might); it is just better for the environment and your wallet to have other paying passengers in your car, rather than you driving alone for hours.
There are also other similar companies and platforms; there are plenty carpooling companies/platforms you can find online.