The number of bikes being used in Leiden is enormous. This is also because most people have more than one bike. Besides the fact that the bike is a real Dutch means of transport, it also the fastest way to get around in Leiden, and it's a part of our culture.
Parking your car is possible in Leiden, in opposite to most other big cities, the parking facilities in Leiden are very good. One example is the "Haagweg" car-park system, you park your car just outside the city centre, and then a mini-bus will take you to the centre. Besides the Haagweg car-park, there are several parking-garages in the centre of Leiden. You can also rent a car, there are several car rental companies in Leiden.
The taxi service in Leiden (and the rest of the Netherlands) is very good though it's expensive. In Holland it's common to order a cab by using the phone, so you call the cab centre and give your address, and within a half-our the cab will pick you up.
The Water Taxi (only for the centre of Leiden)
Water has always played an important role in Leiden. The city is rife with canals and those canals are a pleasant spot for cruise boats, yachts and the Water taxi! Using the water taxi may not be the fastest way to get around it certainly is the most attractive way to see Leiden. The water taxi has various "stops" all over the centre.
Public transport is very good in Leiden, there is an enormous number of bus-stops in Leiden also in the city centre, so using the bus is a good alternative for the car.