Octet rule violation in Period 2 elements
Typically the octet rule becomes less likely to work, regardless of the period, when we move to a group where there are too few valence electrons to go around.  Prominent examples in Period 2 include compounds of beryllium in Group 2 (such as the fluoride, especially when gaseous or liquid) and boron in Group 13 (as in alkyl boranes like this one).  Carbon can also form species that are most stable with fewer electrons than the octet rule would predict, a "violation" most prominently seen in the cyclopropenyl cation, where another "rule" that is much more reliable when properly used comes into play.