Yes. In fact there doesn't need to be witnessess. For instance, if you promise to marry someone and then reneg on the deal you can be sued for breach of contract. Of course proving that you agreed to marriage would be difficult without witnessess.
Keith
yep, mortartube is right, all verbal contracts are legal if they contain the same necessary elements as a documented contract, the only problem is the one you have identified which is evidence of the contract. :-)
Every time you go into a shop and buy something and the the sales assistant asks you for payment it is in effect a verbal contract. You need the 3 main components of a contract - offer, acceptance & consideration (usually payment). However, without witnesses obviously it would be difficult to prove.