Recently, both the ATLAS and CMS experiments have observed an excess of events that could be the first evidence for a 125 GeV Higgs boson. This is a few GeV below the (absolute) vacuum stability bound on the Higgs mass in the Standard Model (SM), assuming a Planck mass ultraviolet (UV) cutoff. In this Letter, we study some implications of a 125 GeV Higgs boson for new physics in terms of the vacuum stability bound. We first consider the seesaw extension of the SM and find that in type III seesaw, the vacuum stability bound on the Higgs mass can be as low as 125 GeV for the seesaw scale around a TeV. Next we discuss some alternative new physics models which provide an effective ultraviolet cutoff lower than the Planck mass. An effective cutoff Lambda similar or equal to 10(11) GeV leads to a vacuum stability bound on the Higgs mass of 125 GeV. In a gauge-Higgs unification scenario with five-dimensional flat spacetime, the so-called gauge-Higgs condition can yield a Higgs mass of 125 GeV, with the compactification scale of the extra-dimension being identified as the cutoff scale Lambda similar or equal to 10(11) GeV. Identifying the compactification scale with the unification scale of the SM SU(2) gauge coupling and the top quark Yukawa coupling yields a Higgs mass of 121 +/- 2 GeV. (C) 2012 Elsevier B.V. All rights reserved.