From eMedicineHealth:

Cold Sore Causes
The virus that causes cold sores is known as the herpes simplex virus (HSV). There are two types of HSV, type I and type II. Cold sores are usually caused by type I. Herpes simplex infections are contagious. The virus is spread from person to person by kissing or other close contact with sores or even from contact with apparently normal skin that is shedding the virus. Infected saliva is also a means of transmitting the virus. People are most contagious when they have active blister-like sores. Once the blisters have dried and crusted over (within a few days), the risk of contagion is significantly lessened. However, a person infected with HSV can pass it on to another person even when a cold sore is not present. This is because the virus is sometimes shed in saliva even when sores are not present. Despite popular myth, it is almost impossible to catch herpes (cold sores) from contaminated surfaces, towels, or washcloths.

From the Mayo Clinic:

Certain strains of the herpes virus cause cold sores. Herpes simplex virus type 1 usually causes cold sores. Herpes simplex virus type 2 is usually responsible for genital herpes. However, either type of the virus can cause sores in the facial area or on the genitals. You get the first episode of herpes infection from another person who has an active lesion. Shared eating utensils, razors and towels may spread this infection.