A spotlight has a setting in the properties window, lamp tab, then under the section "Spot Shape" called "Blend", what does it do?
The tool tip says "Softness of the spotlight edge" yet setting it to zero did not make the lamp's edge noticeably any sharper.

The image on the left the blend is to 0 on the right it is set to .5
spotlight with blend set to 0 spotlight with blend set to .5


TLDR Reduce the size of the lamp (something around 0.01 BU).
settings for the spotlight

The blend value still does what it always did in the blender internal render, make the edges of the spotlight softer.

The reason you can't see much difference when you change the blend value is because of the lamp's size. (Independent from the blend value if you change the lamp's size the light and the shadows will get softer, or sharper.)

Simply set the lamp's size to something very small (around 0.01 BU). Not the angle of the beam, but the size of the lamp (top "Size" field). Now you can adjust the blend value. There isn't that better.

In the picture below both lights have the blend set to 0, but the size is different 1 BU for the pink light, and 0.01 BU for the green light.
two spotlights showing the difference in lamps size

For additional reading the cycles documentation for the spotlight is rather short, we have to go to the BI side of the docs to get more info on the blend setting.

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