There are a few possible places where aircraft/helicopter can do their take-off.
Mostly they are sea-planes that take-off from water. Although most aircraft are prepared to do emergency landing on water, they can not do take off from water, otherwise are specially designed.
B) Airport runway
This is the most common place for taking off. Most of the commercial aircraft operate from there.
C) On rooftop
Motsly done by helicopters, as they do not need much space (they do take off vertically). Most of the modern buildings on big cities have specially designed place on their rooftop for choppers to land (they call this helipad)
D) On a ship
It is common for military aircraft. As the runway is extremely short, it requires much more thrust than if the take off is done on a normal runway
It is commonly done for agricultural purposes. The aircraft are normally realatively small, as they do not need a long runway to take off.