  Observations of high redshift supernovae imply an accelerating Universe which
can only be explained by an unusual energy component such as vacuum energy or
quintessence. To assess the ability of current and future supernova data to
constrain the properties of the dark energy, we allow its density to have
arbitrary time-dependence, $\rho_X(z)$. This leads to an equation of state for
the dark energy, $w_X(z)=p_X(z)/\rho_X(z)$, which is a free function of
redshift $z$. We find that current type Ia supernova (SNe Ia) data are
consistent with a cosmological constant, with large uncertainties at $z\ga
0.5$. We show that $\rho_X(z)/\rho_X(z=0)$ can be measured reasonably well to
about $z=1.5$ using type Ia supernova data from realistic future SN Ia pencil
beam surveys, provided that the weak energy condition (energy density of matter
is nonnegative for any observer) is imposed.
  While it is only possible to differentiate between different models (say,
quintessence and k-essence) at $z \la 1.5$ using realistic data, the correct
trend in the time-dependence of the dark energy density can be clearly detected
out to $z=2$, even in the presence of plausible systematic effects. This would
allow us to determine whether the dark energy is a cosmological constant, or
some exotic form of energy with a time-dependent density.
