That said, it's a slight pet peeve of mine when people recommend the median over the mean to describe center. The median, on its own, does not describe what is "typical" any more than the mean does; it just has a small advantage in that it will always map a real observation, so for discrete data you don't end up with things like "1.9 legs." (That said, a mean of 1.9 legs actually seems much more informative to me than a median of 2 legs, so even in that case I prefer the mean.) It's easy to envision many situations where the median's representation is wildly inaccurate, just as you can imagine ways in which the mean can be misleading.
The median is also insensitive to skew, which is often cited as a good thing, but really that's something you should determine on a case-by-case basis. In many (most?) applications, there's no tangible benefit in having a measure of center that ignores skew. The median's insensitivity also creates strange situations where subgroups in the population end up unrepresented (e.g. if the poorest 20% become even poorer because of changes to the tax code, the median doesn't budge). In general, the median conveys remarkably little information. It's great at showing the center, but it gives zero indication of anything else. The mean certainly has its issues, but it's far from inferior. Use the median when the situation calls for it, certainly, but realize that it's just as limited as any other measure, if not more so.