Among their amazing properties, graphene and related low-dimensional materials show quantized charge-density fluctuations-known as plasmons-when exposed to photons or electrons of suitable energies. Graphene nanoribbons offer an enhanced tunability of these resonant modes, due to their geometrically controllable band gaps. The formidable effort made over recent years in developing graphene-based technologies is however weakened by a lack of predictive modeling approaches that draw upon available ab initio methods. An example of such a framework is presented here, focusing on narrow-width graphene nanoribbons, organized in periodic planar arrays. Time-dependent density-functional calculations reveal unprecedented plasmon modes of different nature at visible to infrared energies. Specifically, semimetallic (zigzag) nanoribbons display an intraband plasmon following the energy-momentum dispersion of a two-dimensional electron gas. Semiconducting (armchair) nanoribbons are instead characterized by two distinct intraband and interband plasmons, whose fascinating interplay is extremely responsive to either injection of charge carriers or increase in electronic temperature. These oscillations share some common trends with recent nanoinfrared imaging of confined edge and surface plasmon modes detected in graphene nanoribbons of 100-500 nm width.