Trojan Horse viruses are what they sound like. They come from the Greek story of the trojan war. Trojan Horses contain a virus, disguised as legitimate software; therefore, the firewall will permit it. For example you might find trojan horses in software that claims to get rid of viruses. Trojan horses, however, are unable to replicate themselves. This is a risk as it is difficult for firewall and humans to detect wether a program is legitmate or is a trojan horse. The possible threats contained in trojan horses are listed below.
This allows hackers to quietly observe what you are doing on your computer and the information you put in it. This is extremely dangerous as they can have acess to your passwords and credit cards etc..
The computer will be bombareded with pop up ads. Constantly offering you their products. This is a marketing tool for the hackers. Adware will look something like this: 
A worm is similar to a virus; however, it can travel from computer to computer without human interation. A worm uses file or information transportation features on your system to allow it to travel un-aided. Worms are able to replicate itself which is extremely dangerous. Worms consume a lot of system memory and network bandwith causing them to crash. Worms allow hackers to control your computer remotely. 
Trojan Horses can include backdoors. Backdoors gives hackers access to your computer, which allows them access to confidential or personal information you have entered on your computer. Such information can be credit cards, bank accounts, and your passwords, maybe even your social number. This gives them the ability to completety rob you in the comfort of their house. All this is done without the user's knowledge. Backdoors can also be found in unauthorized websites. They will act like normal software until they have enough required information, there they will become backdoors.