Definition of a virus
A virus is a program that is able to replicate - that is, create (possibly modified) copies of itself. 
The replication is intentional, not just a side-effect. 
At least some of the replicants are also viruses, by this definition. 
A virus has to attach itself to a host, in the sense that execution of the host implies execution of the virus.

What do I do if my computer becomes infected?

Not every one who thinks s/he has a virus actually does. Reformatting your hard disk is almost certainly unnecessary and very probably won't kill the virus. If you have a good antivirus package, use it. Better still, use more than one. 
 
Follow the guidelines below as far as is practicable and applicable. 
Do not attempt to continue to work with an infected system, or let other people do so. 
users of infected machines should not under any circumstances trade disks with others until their systems and disks are cleaned. 
if the infected system is connected to a network, it should be logged off all remote machines
No files should be exchanged between machines by any other means until it's established that this can be done safely. 
Ensure that all people in your office and anyone else at risk are aware of the situation. 
Get all floppy disks together for checking and check every one. This includes write-protected floppies and program master disks. Check all backups too (on tape or file servers as well as on floppy). 

What is a virus (and what are Trojans and Worms)?

A virus  a program which attaches itself to, overwrites or otherwise replaces another program in order to reproduce itself without the knowledge of the PC user. 
A Trojan Horse is a program intended to perform some covert and usually malicious act which the victim did not expect or want. It differs from a destructive virus in that it doesn't reproduce, (though this distinction is by no means universally accepted). 
A dropper is a program which installs a virus or Trojan, often covertly. 
A worm is a program which spreads (usually) over network connections. Unlike a virus, it does not attach itself to a host program. In practice, worms are not normally associated with personal computer systems.  

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