  Recent results from ATLAS and CMS point to a narrow range for the Higgs mass:
$M_H\in[ 124, 126] {\rm GeV}$. Given this range, a case may be made for new
physics beyond the Standard Model (SM) because of the resultant vacuum
stability problem, i.e., the SM Higgs quartic coupling may run to negative
values at a scale below the Planck scale. We study representative minimal
extensions of the SM that can keep the SM Higgs vacuum stable to the Planck
scale by introducing new scalar or fermion interactions at the TeV scale while
solving other phenomenological problems. In particular, we consider the type-II
seesaw model, which is introduced to explain the non-zero Majorana masses of
the active neutrinos. Similarly, we observe that if the stability of the SM
Higgs vacuum is ensured by the running of the gauge sector couplings, then one
may require a series of new electroweak multiplets, the neutral component of
which can be cold dark matter candidate. Stability may also point to a new U(1)
gauge symmetry, in which the SM Higgs carries non-zero charge.
