Is this static mechanical balance possible without trickery? On damnlol.com, I came across this picture:

http://www.damnlol.com/hello-god-i-have-a-fault-to-report-7549.html
My question is: Is this possible without glue? If not are there similar situations in which something like this is possible ?
 A: Yes, it's possible.
A static setup like this will work as long as any small motion of the parts would increase the potential energy.  In this case, it looks like there is only one possible motion - rotation of the entire ruler-hanger-hammer piece about the axis where the ruler touches the table.
If the ruler were to rotate down a little bit, the entire hammer would go down some, decreasing its potential energy.  However, it would also rotate, raising the head, where most of the mass is, and thus increasing the potential energy.  When these two effects cancel, the system will be in equilibrium.
To figure out when the effects will cancel, we could find the system's center of mass.  If the center of mass is directly under the contact point, the system's in equilibrium.  This is because as the system rotates, the center of mass moves in a circle.  To be in equilibrium, it must be at the bottom of that circle.  The center of the circle is at the contact point, so the bottom of the circle is directly beneath it.
There are other, equivalent ways of doing the same problem.  For examples check out these questions:
Why does the weighing balance restore when tilted and released
Equilibrium and movement of a cylinder with asymmetric mass centre on an inclined plane
