In supersymmetric models with gravity-mediated SUSY breaking, universality of soft SUSY breaking sfermion masses m0 is motivated by the need to suppress unwanted flavor changing processes. The same motivation, however, does not apply to soft breaking Higgs masses, which may in general have independent masses from matter scalars at the GUT scale. We explore phenomenological implications of both the one-parameter and two-parameter non-universal Higgs mass models (NUHM1 and NUHM2), and examine the parameter ranges compatible with ΩCDMh2, BF(b→sγ) and (g−2)μ constraints. We have demonstrated that in contrast to the mSUGRA model, in both NUHM1 and NUHM2 models, the dark matter A-annihilation funnel can be reached at low values of tan β, while the higgsino dark matter annihilation regions can be reached for low values of m0. We show that there may be observable rates for indirect and direct detection of neutralino cold dark matter in phenomenologically aceptable ranges of parameter space. We also examine implications of the NUHM models for the Fermilab Tevatron, the CERN LHC and a (s)1/2 = 0.5−1 TeV e+e− linear collider. Novel possibilities include: very light tilde uR, tilde cR squark and tilde eL slepton masses as well as light charginos and neutralinos and H, A and H± Higgs bosons.