In a word, non-metals (reacting with themselves or each other)
Many non metal elements are diatomic and bond covalently (hydrogen, iodine etc). Others form large covalent networks in what is called a giant structure (carbon, silicon, etc).
In more technical terms, substances bond covalently i.e. share electrons when the difference between their electronegativities (you can find tables of electronegativities easily - see below) is small, typically less than 1.7 or thereabouts.
You will find that non metals have a narrow range of electronegativities and so any non -atomic elements or compounds are going to be covalent.
Metals have low electronegativities whereas non-metals have high electronegativities. This means that typically, when they interact, they form ionic compounds (difference greater than 1.7).
Metals are not deemed to 'react' with each other. At best they 'mix' forming alloys.