Why would this reaction occur? Won't it be unfavourable? I was just reading about how Nitrogen and Oxygen combine to form Nitric oxide. 


My question is, why would this reaction even occur? Isn't the valency of Nitrogen 3- and Oxygen 2-, and therefore this reaction seems to form a product that still hasn't achieved the octet electronic configuration.
Could I please have some help?
Thank you in advance.

Edit: Or even $\ce{N2O}$ or $\ce{NO2}$ for that matter?
You're right: $\ce{NO}$ is a free radical and the reaction between $\ce{N2}$ and $\ce{O2}$ can be achieved - supposed that enough energy is provided.

This may happen through an electrical arc discharge in the lab or, in the mesosphere (50-85km above earth) through ionizing cosmic rays. Note however that nitric oxide react with oxygen to eventually furnish nitrogen dioxide $\ce{2 NO + O2 &lt;=&gt; 2 NO2}$.