It has been a long time since then, viruses present a far bigger problem now, but there is still no exact definition of a computer virus, despite many attempts to give one.
The main difficulty while trying to give the exact definition of a virus is that virtually all the unique features of a virus (incorporating with other objects, stealth behavior, potential danger and so on) may be found in other non-virus programs, or there exist some viruses which are free from those features (except for their spreading capabilities).
For example, if we take stealth capability as a distinctive feature of a virus, then it's easy to give example of virus not denying its spreading. Such a virus before infecting any file outputs a message saying that there is a virus in a computer ready to hit another file, then outputs its filename and prompts for user permission to incorporate itself into this file.
If we take the ability to destroy programs and data on disks as a distinctive feature of a virus, then as a counter-example for this feature it's possible to give the dozens of absolutely harmless viruses, which do nothing but spread themselves.
However the main feature computer viruses - their capability of incorporation into different objects of operating system - can be found in many conventional programs, which are not viruses. For example, the most widespread operating system MS-DOS has all the necessary means to arbitrarily install itself to non-DOS disks. To do so it is sufficient to create an AUTOEXEC.BAT file containing the following lines:

SYS A:

COPY *.* A:

SYS B:

COPY *.* B:

SYS C:

COPY *.* C:

...


on a DOS boot floppy.
If you modify DOS as described above, it will become a virus in its own right from the point of view of any existing definition of a computer virus.
Thus the first reason not allowing us to give an exact definition of a virus is the impossibility to name features which virus and only virus can have.
The second difficulty arising when trying to work out the definition of a computer virus is the fact that this definition has to be OS-specific. For example theoretically there can be operating systems in which viruses simply cannot exist. This may be the system where it is prohibited to modify executable code, i.e. those objects that are already being executed or can be executed by operating system under certain conditions.
Therefore it is possible to give only the necessary condition for considering some sequence of executable code a virus.
THE NECESSARY CONDITION OF BEING CONSIDERED A COMPUTER VIRUS is the capability to produce copies of itself (not exact bytewise replicas) and to incorporate them into computer networks and/or files, system areas of computers, and other executable objects. In addition to that copies also maintain the capability to spread further.
It has to be mentioned that this condition is not sufficient (i.e. final), because for example the MS-DOS operating system has the necessary condition of a virus, but is obviously not a virus.
This is why there is no exact definition of a virus up to this moment, and it can hardly be given in the near future.