Is it required for pilots to contact ATC while flying VFR?
It depends on which class of airspace you are flying in. For airspace classes A, B, C and D, a continuous two-way radio contact with ATC is required for all VFR flights. In airspace classes E, F and G, there is no such requirement.
The below table shows requirements for both IFR and VFR to fly in different airspace classes (source: ICAO Annex 11, Appendix 4). You should notice the second column from the right, which specified the radio communication requirements for a given airspace class.

These are general rules, that apply to all ICAO member states (basically, every country in the world), unless a specific state has decided to deviate from the ICAO standards. Such deviations will be listed in the national AIP, section GEN 1.7. For example, in some countries, two-way radio communication may be required for VFR traffic within certain airspaces classified G, even though that is generally not the case. A table with rules specific for your country will be available in your national AIP, section ENR 1.4, and will probably look quite similar to the above.
At controlled airports, a control zone will be established, which will be class A, B, C or D (cf. ICAO Annex 11 para 2.6, a control zone cannot be classified E). This means that, at a controlled airport, VFR traffic must establish a two-way radio contact with ATC, just like IFR.
At uncontrolled airports, however, this is generally not required.
During the approach, departure and en-route phases of flight, whether or not you are required to be in contact with ATC depends entirely on where you are flying. Very generally speaking, if flying close to controlled airports or above a certain level, you can expect the airspace to be controlled, and thus, contact with ATC is required. At low altitude, away from major airports, the airspace will often be uncontrolled, and no radio contact required.
The above is a very general description, and you really must refer to local charts and procedures to figure out if you are required to contact ATC in a specific area.
As a point of advice, ATC is there to help you. It is a good idea to contact ATC even if you are not required to do so, in order to receive flight information service and alerting service. This allows you to receive important information about traffic, weather, military activity, etc., and if something happens to you, a search and rescue mission can be initiated without delay.