Prediction: lots of emerging startups who are basing their code on Python today are going to resort to this (or PyPy, but that's unrelated) when the scaling pain begins, or simply to attempt making things run a bit faster. I think this is great. Most people I know avoid C completely because of the hidden pitfalls every novice has to go through, but maybe Cython will slowly change that. It just needs a bit more maturity and some endorsements to pop up around here... which shouldn't take too long.
With C and Python you get to play on both ends of the spectrum -- concise clear code, and high performance code with C.
Cython is interesting, but as cited, there are also some limitations and caveats. See http://docs.cython.org/src/userguide/limitations.html and http://docs.cython.org/src/tutorial/caveats.html
About playing on both sides of the efficiency/expressiveness spectrum, the important thing is to be sure to do real benchmarks so you only drop down into C when it pays off.
Sometimes, the reasons are not just efficiency -- you may already have C code that does the right thing.
In that case, however, you should very definitely (as in, I'm not even considering an alternative) go with Python/Cython, as you will develop many times faster and your program will have near-C speed.
My current favorite is ShedSkin, which compiles your (unmodified) program written in a subset of Python (not a particularly limiting subset, mind you) into C++ which you can then compile (and link as a module, if you like).
My experiences with both: