Named for the infamous, deceptive peace offering of the Grecian army during the Trojan War, a Trojan Horse virus operates much the same way; it masquerades as a friendly, peaceful program when, in reality, it's much more destructive.
There are a variety of effects attributed to a Trojan Horse program, none of which bode well for the recipient computer.
Once it's in your system, a popular trick of a Trojan Horse is to implement a "keylogger" program. Such programs register which buttons and keys you press on your keyboard, and send a report of them to the hacker.
For example, if you access your online bank account, enter your credit card information for online purchases, or transmit other important, confidential information--the keylogger sends it all right to the hacker.
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The target of these hackers is your personal--usually financial--information.
Some particularly malicious Trojan Horses are programmed to attack their victim's computer.
The Trojan could corrupt very delicate data at the core of your operating system, causing everything from minor glitches to an operating system crash.
The hackers who create these Trojans seem to be interested in vandalism--the wanton, malicious destruction of another person's property.
Remote Access (Backdoor)
The final--and possibly most detrimental--version of the Trojan Horse is one that installs a remote access program to your computer, also known as a "backdoor."
This backdoor gives the hacker access to your computer system, allowing her to peruse, change, or delete your personal files at her leisure.
These hackers might be after anything; financial data, personal information, destruction--or all three. Remote Access Trojans are by far the most powerful and dangerous viruses your computer can contract.