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How can I rotate a Hermi light source so that it shines towards a specific object or the location of the 3D cursor?

Bonus if the light source adjusts its orientation if I manually move the tracked object.

It don't have to work for animations, I've got only a static scene.

I already tried the Object Constraints "Track To" which was mentioned in a similar question but I have to choose between X, Y, Z axis but I want all three?! Am I just using it wrong?

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You can't track to the 3D cursor but can easily track the lamp to an object via the Track To constraint.

Select the Hemi lamp and add the Track To constraint as follows :

Track To

Here I've set the Target to an Empty. Note that the To is set to '-Z' and Up is set to X (but could just as easily been Y - it must not be set to the same axis as To otherwise the constraint is invalid and will not work).

Moving the Empty will now automatically orient the lamp to point to the Empty. This will work equally well for Sun, Spot, and Area lamps but is obviously not generally relevant for Point lamps (since they don't have direction).

It is unfortunately not possible to automatically point the lamp to the 3D cursor (except, perhaps using a python handler) but this shouldn't be necessary as it's a simple case to move the Empty to the 3D cursor via the Snap-To menu (Shift-S, Selection to Cursor).

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    $\begingroup$ Thanks, I needed to read the Blender Wiki page twice after seeing that it indeed works to understand that a lamp is a 3D object like any other and thus cannot face towards the target with all its sides at the same time. So I have to choose the one of its 6 sides ("local axis"). $\endgroup$ – lathspell May 5 '17 at 21:18

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