Trojan – is a program which is used to gain access to a computer by installing a program on infected PC to open some backdoor. [Trojans are also known as Backdoors].
Worm – is a program which infects the computers which are connected by some network. Worms slow down the network.
Spywares – are the program which are used to monitor/Log the activity performed on a computer. These are used to spy on some one either for legal or illegal perpose. Example: Keylogger applications.
Adwares – are the programs which delivers ads to your computer (generally in POP-UP's form). They consume your network.
Malwares – are the program with malicious intention. It can be damaging your computer, spying on you or any other malicious task.