The octet-rule is a very inadequate rule for understanding overall reactivity.
Ultimately you need to understand two things to know whether reactivity is likely: the thermodynamics of any possible reaction; and the kinetics of any possible reaction mechanism for the reaction.
The formation of many oxides is thermodynamically favourable. That's why many compounds burn in an atmosphere containing oxygen. The formation of sodium oxide, carbon dioxide and many metal oxides is thermodynamically favourable. Carbon-containg things will burn in air, metals will often react (quickly, like sodium, or slowly, like iron). Some will burn spontaneously like caesium; others will take a little encouragement.
The second factor that matters is whether there is an easy way for the oxidation reaction to happen. Aluminium, for example, is very reactive but rapidly forms a protective layer of strong aluminium oxide (alumina) on the surface preventing further reaction; iron is relatively reactive but won't rust easily unless contaminants are present; gold won't react at all. Carbon needs to be heated to start the reaction but will burn by itself when it does start.
Where reactions have easy to access mechanisms and some thermodynamic advantage, oxygen is very reactive.
Another thing to remember about oxygen is that it has some reaction mechanisms that are less than obvious and easier than expected for a diatomic molecule. Unlike nitrogen, for example, where thermodynamically favourable reactions are inhibited by its strong triple bond (and filled octet) an oxygen molecule is actually a diradical: despite the apparent filled octets you would expect from simple electron counting, the molecule has two unpaired electrons (this requires a bit of molecular orbital theory to explain and is one of the observations that simple electron octet counting doesn't explain well). Radicals tend to be more reactive than paired electron orbitals (or filled octets).
In short, an octet-counting view is too simplistic to explain oxygen's reactivity and you need more sophisticated ways of looking at the electronic structure. And don't forget that you also need to know the thermodynamics and the kinetics of potential reaction mechanisms to get any useful predictions of whether reactivity is likely.