Structure of $\ce{SO3}$ (sulfur trioxide):
In the molecule, if each oxygen atom shares two electrons with sulfur atom then how does the sulfur atom remain stable? It already has 6 valence electrons and needs only 2 more to become stable but the oxygen atoms share total of 6 electrons with sulfur atom. So how is the molecule stable?
Synthesis of $\ce{SO3}$ can be done by heating $\ce{CaSO4}$ with $\ce{SiO2}$, which produces $\ce{CaSiO3}$ and $\ce{SO3}$. Another way of synthesis is the heating of $\ce{NaHSO4}$ to $\ce{Na2SO4}$, $\ce{SO3}$, and water. (source)
Sulfur forms an expanded octet. That means that it doesn't really obey the octet rule, allowing it to take on extra electrons. Sulfur is a 3rd-period element; hence it can use its 3d orbitals to make more than 4 bonds. Wikipedia has a page on hypervalency, and from an answer here:
Regarding the octet concept, it's only a guideline at best, and nothing more. I wouldn't put too much stock into the concept. If you insist on using it, then only apply it to the following elements: C,N,O, and F.
EDIT:
Users such as @Mithoron have pointed out that this analysis is not correct. Papers seem to show that there is no d-orbital utilization. According to this comment:
...the doubly bonded picture is a very crude oversimplification, though. -@Martin
This enlightening image 
shows that sulfur trioxide is actually a resonance of several different structures, and should be more accurately expressed as several single bonds with a dashed line to show that the bond order is not actually two. This also solves the question as to why it is stable with apparently six bonds, as in reality it only has four bonds.
In the molecule, if each oxygen atom shares two electrons with sulfur atom then how does the sulfur atom remain stable?
Look at the structure of Xenon tetrafluoride $\ce{XeF4}$ and Xenon hexafluoride $\ce{XeF6}$. Do the Fluorine donate any electron to the Xenon? Of course not. It is the other way, the Fluorine with 7 electrons in the second shell needs one more electron to fulfill tho noble gas configuration and the Fluorine takes this electron from the Xenon with its electrons in the fifth shell. You know, the ionisation energy is higher in low electron shells, this allows to compose these compounds.
The same happens to the sulphur atom with its 6 electrons in the third shell. The three oxygen atoms fulfill their shells at the expense of sulphur. And sulphur gets closer to the level of the noble gas Neon. Of course this is a oversimplification because the atoms share the electrons.
The sulfur element has D-shell available for bonding. That is why it can form six bonds and have an expanded octet. Oxygen on other hand uses p shell for bonding which is completely filled by sharing 2 electrons. As to why sulfur expands, sulfur has vacant d orbitals lying with comparable energy to the bonded ones hence it is energetically favorable to form more bonds. Also, note that typically atoms with large sizes form expanded octet with small surrounding atoms as there is less inter-electronic repulsion.
