  In this paper we present the results of measurements of the microwave surface
impedance of a powder sample and two films of MgB$_2$. One film has $T_c=30$ K
and is not textured, the other is partially c-axis orientated with $T_c=38$ K.
These samples show different types of temperature dependence of the field
penetration depth: linear for the powder sample, exponential with
$\Delta/kT_c<1.76$ (film with $T_c=30$ K) and strong coupling behaviour with
$\Delta/kT_c\sim 2.25$ (film with $T_c=38$ K). The results are well described
in terms of an anisotropic gap model or presence of a slightly deficient
MgB$_2$ phase. The data set for all samples - taken as a whole cannot be fitted
into a two gap scenario.
