  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
paper, 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
dicuss some alternative new physics models which provide an effective
ultraviolet cutoff lower than the Planck mass. An effective cutoff \Lambda
\simeq 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 allows us to predict a Higgs
mass of 125 GeV, with the compactification scale of the extra-dimension being
identified as the cutoff scale \Lambda \simeq 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\pm 2 GeV.
