Theoretically, wingtip vortices will start as soon as there in any pressure differential between the upper and lower surface if the wing, so even parked, facing into wind there will be small very weak vortices being formed.
When an aeroplane with a nosewheel is on the ground, the wing will have a very small angle of attack and therefore there won't be much of a pressure differential between the upper and lower surface of the wing. As the aircraft begins to move down the runway, the pressure differential will increase a small amount (ever notice how on large aircraft the wings begin to flex even before rotation?). At rotation the angle of attack is increased hugely, the pressure differential increases hugely and air below the wing attempts to move around the wingtip to the area of comparatively low pressure above the wing. As the aeroplane is moving at a relatively slow speed (compared to in the cruise) the vortices form over a short space and thus are more intense.
In the cruise there is the aircraft travels at a higher speed but lower angle of attack. There is the same pressure differential between the upper and lower wing surfaces as at rotation but the vortices are "stretched" over a longer horizontal distance and are therefore less intense. Landing has the opposite effect of takeoff; as the nosewheel is lowered to the runway surface, the angle of attack decreases and the pressure differential between the upper and lower surface of the wing decreases.
The use of flaps will decrease the intensity of wingtip vortices as vortices shed from the flaps will tend to mix with and disrupt the wingtip vortices.
sr
Aah Sir Pratt, you beat me to it.....