One of my favorite stylized facts about development is contained in the graph below, which comes from a paper by Imbs and Wacziarg. What it shows is that as countries grow out of poverty, their economies become less specialized and more diversified. This seems to be true both across countries, and within countries over time.
What's the big deal, you might say. Well, it is a big deal if you have been brought up on the idea that the key to economic growth for poor countries lies in specialization according to comparative advantage. If that simple recipe were true, countries that are getting richer would be producing a narrower range of goods, not a broader range. It takes a lot of mental gymnastics to square this stylized fact with the standard comparative advantage arguments. A far simpler interpretation is that the key to growth is the acquisition of production capabilities in an increasing range of goods, in a way that is often in tension with what comparative advantage would dictate. Here is a paper that tries to make these ideas more precise.
The Imbs and Wacziarg data show that countries do begin to specialize after some point (and hence the U-curve in the graphs), but that point comes relatively late in the development process, once Ireland's level of income is reached.
UPDATE: Roberto Porzecanski's comment below provides an opportunity for clarification. Roberto says the Imbs-Wacziarg result is consistent with trade models, insofar as countries that are growing through capital-deepening may end up producing a broader menu of goods as a result. Yes, of course. But my concern is not whether this stylized fact is consistent with trade models (it certainly is), but whether it is consistent with a story about trade and trade policy being a causal driver of growth. If countries that are growing are those that are making use of comparative advantage while those that aren't are not, then you should see the growing group of countries becoming more specialized. The standard trade-based story is that accumulation and productivity change are the result of an increase in the economy-wide return to such activities, driven by comparative advantage (and therefore specialization). So you should see, at least over part of the lower-income range, a positive relationship between specialization and incomes.
"A student" asks whether non-homotheticity of demand can explain the I-W result. I don't quite follow, and I don't see how it could.
For more potential explanations, you should turn to the original Imbs-Wacziarg paper in the AER (2003).