Does the mass of the observable universe ever change?

Even if you're only referring the "ordinary" matter (such as stars, gas, and bicycles) and dark matter, the mass of the observable Universe does increase, not because mass is being created, but because the size of the observable Universe increases. In a billion years from now, we can see stuff that today is too far away for the light to have reached us, so its radius has increased. Since the mass $M$ equals density $rho_mathrm{M}$ times volume $V$, $M$ increases.

As called2voyage mentions, we have several ways of measuring the density, and we know it's close to $3times10^{-30},mathrm{g},mathrm{cm}^{-3}$. The radius is $R = 4.6times10^{28},mathrm{cm}$, so the mass is
$$M = rho_mathrm{M} frac{4pi}{3}R^3 simeq 10^{57},mathrm{g},$$
or $5times10^{23}M_odot$ (Solar masses).

However, another factor contributes to the mass increase, namely the so-called dark energy, which is a form of energy attributed to empty space. Since the Universe expands, dark energy is being created all the time.