The term comes from the a Greek story of the Trojan War, in which the Greeks give a giant wooden horse to their foes, the Trojans, ostensibly as a peace offering. But after the Trojans drag the horse inside their city walls, Greek soldiers sneak out of the horse's hollow belly and open the city gates, allowing their compatriots to pour in and capture Troy.

Trojan horses are broken down in classification based on how they breach systems and the damage they cause. The seven main types of Trojan horses are:

• Remote Access Trojans
• Data Sending Trojans
• Destructive Trojans
• Proxy Trojans
• FTP Trojans
• security software disabler Trojans
• denial-of-service attack (DoS) Trojans

Also see The Difference Between a Virus, Worm and Trojan Horse  in the Did You Know? section of Webopedia.

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Webopedia's "Did You Know?" Article
The Difference Between a Virus, Worm and Trojan Horse.