Backdoor: A secret computer program that gives its creator a method of gaining access without a password to a computer system or computer network, often allowing the infected system to be used in later attacks.
Trojan Horse: A program that evades security and masquerades as something harmless. Unlike viruses, Trojan horses do not replicate themselves, but they can be just as destructive.
Virus: A malicious program or piece of software code that attaches itself to a computer program, usually with unwitting assistance from the computer user. Viruses can replicate themselves, which potentially can clog the system until it stops working. Some viruses destroy data, transmit themselves across networks, and bypass security systems.
Worm: A type of virus that can replicate itself over a computer network and usually performs malicious actions, such as using up the computer’s resources and potentially shutting the system down. Hybrid worms may contain viruses, backdoors, and Trojan horses.
SOURCE: Adapted from Webopedia.com and other sources