Recently discovered two-dimensional (2D) boron polymorphs, collectively tagged borophene, are all metallic with high free charge carrier concentration, pointing toward the possibility of supporting plasmons. Ab initio linear response computations of the dielectric function allow one to calculate the plasmon frequencies (omega) in the selected example structures of boron layers. The results show that the electrons in these sheets indeed mimic a 2D electron gas, and their plasmon dispersion in the small wavevector (q) limit accurately follows the signature dependence omega proportional to root q. The plasmon frequencies that are not damped by single-particle excitations do reach the near infrared and even visible regions, making borophene the first material with 2D plasmons at such high frequencies, notably with no necessity for doping. The existence of several phases (polymorphs), with varying degree of metallicity and anisotropy, can further permit the fine-tuning of plasmon behaviors in borophene, potentially a tantalizing material with utility in nanoplasmonics.