What is the legal status of a verbal contract?

It depends upon the jurisdiction. In many places a verbal contract is just as good as a written one in the eyes of the law - it is an enforceable agreement. However, it can be harder to prove the terms of a verbal agreement in court as both sides may (and usually will) have different recollections. The plaintiff must show some convincing evidence in order to prevail.

However, in some countries contracts are not enforceable unless they are in writing (in some countries the rule only applies to certain types of contract - for example, in England, verbal contracts are enforceable except if they relate to the transfer of land, where a written contract is required). Also be aware that in some countries (particularly South American and Eastern Europe) many contracts cannot be enforced unless they have been notarised, and clearly you can only notarise a written contract.