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What shape for the edges of a pot and what surface properties are best for a tea pot not to spill? Apart from the cross-section from the side, how does the radius of curvature as seen from above play a role? Ideally it should also stop drops coming down. And how does that depend on the properties of the liquid inside?

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This is too open a question. Is it while walking? using? spill from the sprout or from the top? A rule of thumb is that a glass/pot/whatever spills less the smaller the possible wavelength of the waves at the surface of the liquid is. That is why if you are carrying a full cup of coffee it is wise to put a spoon in it: it halves the possible wavelengths and as the energy transmitted to the liquid is the same, the possible height is halved. A teapot has a complicated geometry, but I would guess the smaller the opening the better. If it is the sprout, it will involve its curve and finish. –  anna v Apr 7 '12 at 11:38
    
If you have questions about details just ask. After you have poured the liquid there are often drops dripping. Some cans do that. Some don't. –  Gerenuk Apr 7 '12 at 12:20
    
Cans? I thought teapots are short and stout and mainly made of ceramic. –  anna v Apr 7 '12 at 13:01
    
For drops to form after the flow is cut,the surface tension of the liquid/surface interface will come into play. Tea spouts have a sharp upward tilted ending that discourages drips. Cans with sharp edges will also discourage them. –  anna v Apr 7 '12 at 14:31
    
Sharp edges could be part of the answer. I also see different shapes and angles. Moreover it seemed to me an elliptic container drips less from the flatter side. What about the material? And why the fancy shapes of teapots openings? –  Gerenuk Apr 7 '12 at 16:25

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The phenomenon you are asking about is known as the "teapot effect". The mystery is why tea dribbles down a pot's spout despite relatively high Weber numbers being associated with the flow. Such high Weber numbers indicate inertia should dominate over surface tension. Recent research has indicated the physics of pouring tea is more complex and does involve surface tension and contact angle effects due to these influencing the flow geometry even at high Weber numbers.

So although particular spout geometries (sharp edges) do help, the elimination of the teapot effect lies in the use of superhydrophobic spouts. The authors of the 2009 paper demonstrate that this completely eliminates any tea dribbling down.

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There exists a description of the published article "Walking with coffee: Why does it spill?"

It is a study experimentally and by models of fluidity, as the title says, of the motion of coffee as one walks with a cup. It does not directly answer the question above, as it is not talking of drops after pouring the liquid.

It gives ways to control coffee spilling,

The best way to prevent coffee spilling might be to find an unusual cup. According to Krechetnikov, ideas from liquid sloshing engineering studies, which historically were done to stabilize fuel tanks inside missiles, indicate three possibilities for spill-free cup designs: "a flexible container to act as a sloshing absorber in suppressing liquid oscillations, a series of annular ring baffles arranged around the inner wall of the container to achieve sloshing suppression, or a different shape cup.

I still think that my aunt's suggestion at church tea parties to put the spoon in the teacup when taking it to the seated aunts is the best way not to spill it :).

Going back to the original question I will summarize my comments in "it is the edge" and that is why a lot of ingenuity has gone into designs of tea spouts available in the market. I have a cheap one liter water heater which has a plastic container. In the beginning it did not drip, but after two years the spout has deteriorated, not visibly, but obviously since it is now dripping. Either the heat or salt accumulation has changed the edge.

Edit: the ruminations of a chemical engineer turned potter on how to make drip free spouts

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the engineer/potter in the link above does make the observation given in @Johannes answer of hydrophobic materials. –  anna v Dec 23 '12 at 9:19

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