Does surface tension play a role in planet's shape? I'm thinking that when the planets and stars were forming  along with gravity surface tension also could have played a role in making them spherical.
Am I correct? 
 A: Let's throw some numbers at this. The Eotvos (or Bond) number is a dimensionless ratio of the body forces to surface tension forces often used in the sciences to characterize certain flows regimes. This number is given by:
$$\mathrm{Eo}=\frac{\Delta\rho g L^2}{\sigma}$$
where $\Delta\rho$ is the density differences between two phases, $g$ is the acceleration of gravity, $L$ is some length scale and $\sigma$ is the surface tension.
Now we need some numbers and some simplifications, let's assume the earth is 100% water then $\Delta\rho\sim10^3\:\mathrm{kg/m^{3}}$, and $\sigma\sim10^{-3}\:\mathrm{N/m}$. The radius of the earth is estimated at $L\sim10^7\:\mathrm{m}$. Together with a value of $g\sim10\:\mathrm{m/s^2}$, it is easy to see that $\mathrm{Eo}\gg1$ or that body forces are MUCH more important than surface tension on the scale of planets and stars. 

TLDR: Surface tension is negligible compared to gravity on the scale of planets.

A: The gravitational binding energy for a spherical object of mass $M$ and radius $R$ is given by:
$$E_{grav}=\frac35 \frac{GM^2}{R}$$
The interfacial energy for a spherical droplet is simply proportional to its surface area:
$$E_{surf}=4\pi \sigma R^2$$
Here $\sigma$ denotes the droplet's surface tension.
Taking the ratio of the two energies and using $M = \frac{4 \pi}{3}R^3 \rho$, it follows that
$$\frac{E_{grav}}{E_{surf}} = \frac{GM\rho}{5\sigma}$$
The mass $M_c$ above which gravitational binding dominates over surface tension is:
$$M_c = \frac{5 \sigma}{G\rho}$$
Considering $G=6.7 \times 10^{-11}~\frac{\text{Jm}}{\text{kg}^{2}}$ and typical values $\sigma \approx 10^{-3}~\frac{\text{J}}{\text{m}^{2}}$ and $\rho \approx 5 \times 10^3~\frac{\text{kg}}{\text{m}^{3}}$, it follows that $M_c \approx 1.5 \times 10^4~\text{kg} = $ 15 tonnes. Therefore, in planet formation surface tension is entirely negligible.
