A Non-Coding RNA, abbreviated ncRNA, is a ribonucleic acid (RNA) molecule which is either not translated into a protein or can be translated into a protein but is biologically active in its RNA form.
Major ncRNA families include ribosomal RNAs (rRNAs), transfer RNAs (tRNAs), small nuclear RNAs (snRNAs), small nucleolar RNAs (snoRNAs), PIWI-interacting RNAs (piRNAs), small interfering RNAs (siRNAs), microRNAs (miRNAs), or long non-coding RNAs (lncRNAs) like the prototypic examples XIST or HOTAIR .
Ref: Palazzo, A. F., & Lee, E. S. (2015). Non-coding RNA: what is functional and what is junk? Frontiers in Genetics, 6, 2. http://doi.org/10.3389/fgene.2015.00002
Historical Perspective on ncRNA discovery
Read review on non--coding RNAs in Arabidospis 
There are many different non-coding RNA families classified according to their origin, genetics pathway and modus operandi .