In amides, there is a barrier to rotation due to the partial double bond character of the bond, but it is not as high as the barrier to rotation of a true double bond. In most cases, it is still high enough that it doesn't occur readily at room temperature.
There may also be a difference in stability between the cis and trans isomers, especially on secondary amides, which would prevent rotation.
Depending on substituents, solvents, and other effects, it is possible to lower the double bond character still further and rotation may be rapid at room temperature.
For true double bonds, you have to provide enough energy to completely break the pi bond in order to get rotation to occur - during the rotation, there is a point where the p orbitals on the two atoms in the bond are at 90 degrees to each other and cannot overlap at all.