Engineering projects that dwarf the imagination, most megascale projects would cause the average left-wing environmentalist to run screaming in terror. Forget about building a dam that may flood wetlands--there have been proposals floated1 for the construction of a 20 mile high wall around Florida to deflect hurricanes from population centers.

Some commonly mentioned megascale projects are:

Alter another world to more closely match our needs. In principle it's no different than building a house or stitching animal skins together to make a blanket; in practice it probably can only be called an environmental nightmare and an ethical dilemma of immense proportion. Available to late type 0 civilizations (such as ours).
Space Elevator
A 20,000 mile high cable with a large asteroid hooked onto the far end to act as a counterweight. Almost certainly available to type I civilizations, probably not available to late type 0s.
Dyson Sphere
A shell made up of billions of floating islands of matter surrounding a star in all dimensions. This configuration allows a civilization to trap something very close to the complete energy output of its primary. Available to type II civilizations.
Stellar Husbandry
Treating stars as we presently treat plants. Probably not available to any civilization short of a late type II.
Jupiter Brain
An "individual" whose computational structure requires a computer with the mass of Jupiter. Such a creature would be of a complexity so vastly greater than that of a human that it is hard to comprehend. Available to advanced type IIIs.

1- Where "floated" is taken in the same sense that proposals for the construction of a Dyson sphere have been floated.