The outer electron shell of all of the noble gases (Neon, Argon, etc) have a complete octet (except helium which only has and only needs two electrons to complete its valence shell) which makes them very stable and nonreactive. The metals on the left (Na, Li, etc) all contain just one electron in their outer shell which makes them unstable and they tend to form ionic bonds.
Note that the column of elements just to the left of the noble gases (the rightmost column save one), the halogens, is also highly reactive, because the halogens all only need a single elecron to form the "stable octet" in the outer shell.
