Why don't elements in Group O (noble elements) react with other elements?

They're not Group O (oh) but Group 0 (zero) elements, but I'm sure
that was just a harmless typo. The reason why this group of elements
is least reactive, and known as the noble or inert group of elements,
is because their last electron shell using the Bohr model is complete
(i.e. 8 electrons for all but He which has 2). This makes them very
stable, and it requires a lot of energy to knock off an electron so
that they are able to bond.

Here are two webpages which explain it in greater detail:
http://www.chem4kids.com/files/elem_inertgas.html
http://www.wpbschoolhouse.btinternet.co.uk/page03/Noble_Gases.htm


Thank you for your question

skermit-ga

Actually, noble gases can react to form compounds, a fact known for
very many years now.  Xenon hexafluoride was one of the first such
compounds to be made.

I refer you to http://www.chemsoc.org/exemplarchem/entries/2001/robson/raregascompounds.htm
for some history.  In 1962, Neil Bartlett made the first compound of
xenon.  In 1933, Linus Pauling (unique recipient of two unshared Nobel
prizes) predicted these compounds.

The comment about the last electron shell being complete is
misleading.  The first two subshells (s and p) are full.  Only helium
(with just an s subshell) and neon have their last electron shell
full.  Importantly, this arrangement does create a situation with low
energy suitable for stability.

Filling argon's last electron shell would require 10 more electrons. 
Before these are added, however, two electrons go into the 4s
subshell, making potassium and calcium along the way.  Nickel (atomic
number = 28) resides where the 3 shell should be full.  The subshell
energetics determine the reactivity and stability of elements.

The comment about Argon's last electron shell not being filled is
misleading.  The valence (in this case the 3p) shell is what is
important when considering reactivity according to valence-bond theory
and is filled on an uncharged Argon atom in its ground state.  If one
wanted to consider all of Argon's shells, you could not stop at the 3d
(the 10 electron shell chempers refers to) because electron shells are
a theoretical idea of where an electron could possibly orbit and not
little compartments around a nucleus where electrons can hang out. 
Therefore, any element has an infinite number of theoretical shells,
not limited to a specific quantum energy such as 3 (3s,3p,3d shells). 
If one could impart significant energy to an electron in Argon's 3p
shell, it could theoretically be promoted to any energy level (even
higher than 3d), as long as there were not other atoms around (as
would be the case here on earth and anywhere but a vacuum).

It is also important to remember that valence-bond theory is just a
theory, not a set of strict rules.  Its ideas are useful in organic
chemistry, but not as much so in other areas of chemistry.  Molecular
orbital theory, crystal field theory, and so on etc. are other, more
recently developed ways of thinking used to explain bonding in other
areas of chemistry such as that of the noble gas compounds in
question.  Valence-bond theory would not be useful in a description of
the bonding in these species, but does a good job of describing why
compounds involving noble gases are rare.

So it is important to remember that using VALENCE-bond theory, it is
the element's VALENCE shell that counts, and consideration of higher
energy unoccupied orbitals doesn't come into play unless you are using
molecular orbital theory, which (I'm guessing the original question
came from a chemistry student) you won't get to enjoy the delights of
until you take undergraduate inorganic chemistry, which you should
it's fun:)  Good luck!

Noble gases can also form excited molecules called excimers.  The
noble gas atoms form an excited dimer molecule, "non-bonding" in the
ground state.  These molecules are used in an Excimer Laser because
they are very efficient in generating UV coherent radiation.