  We report a significant enhancement of the upper critical field $H_{c2}$ of
different $MgB_2$ samples alloyed with nonmagnetic impurities. By studying
films and bulk polycrystals with different resistivities $\rho$, we show a
clear trend of $H_{c2}$ increase as $\rho$ increases. One particular high
resistivity film had zero-temperature $H_{c2}(0)$ well above the $H_{c2}$
values of competing non-cuprate superconductors such as $Nb_3Sn$ and Nb-Ti. Our
high-field transport measurements give record values $H_{c2}^\perp (0) \approx
34T$ and $H_{c2}\|(0) \approx 49 T$ for high resistivity films and
$H_{c2}(0)\approx 29 T$ for untextured bulk polycrystals. The highest $H_{c2}$
film also exhibits a significant upward curvature of $H_{c2}(T)$, and
temperature dependence of the anisotropy parameter $\gamma(T) = H_{c2}\|/
H_{c2}^\perp$ opposite to that of single crystals: $\gamma(T)$ decreases as the
temperature decreases, from $\gamma(T_c) \approx 2$ to $\gamma(0) \approx 1.5$.
This remarkable $H_{c2}$ enhancement and its anomalous temperature dependence
are a consequence of the two-gap superconductivity in $MgB_2$, which offers
special opportunities for further $H_{c2}$ increase by tuning of the impurity
scattering by selective alloying on Mg and B sites. Our experimental results
can be explained by a theory of two-gap superconductivity in the dirty limit.
The very high values of $H_{c2}(T)$ observed suggest that $MgB_2$ can be made
into a versatile, competitive high-field superconductor.
