How relevant is the concept of ‘class’ to research in politics or political economy today?

Answer 1

It depends on the society and your definition of "class".

In industries where social mobility is low, class is still a very important concept.
http://en.wikipedia.org/wiki/Social_class

In some industrialize countries, such as England, it is still a major factor:
http://www.victorianweb.org/history/Class.html

(In "My Fair Lady", Prof. Higgins sings "An Englishman's way of speaking absolutely classifies him". That was right on then and is still pretty much true (as is the next line, "As soon as he opens his mouth, he makes some other Englishman despise him")

The situation in the U.S. is more complex:
http://en.wikipedia.org/wiki/Social_class_in_the_United_States

One reason is that there have been so many other social divisions affecting political behavior (race, country of origin, religion, etc.)

Another is that the economy has moved away from the old occupations into the service industries, etc. blurring some of the distinctions between the "working class" and the "middle class", it blurs people's perceived interests.

Still another is the social mobility that has been available, to at least some extent, through the school systems (no other country has had such a high percentage of people going to college, etc.)

And then there is the fact that so many Americans think of themselves as "middle class". Since traditional class boundaries were recognized by the people as well as by the researchers, they provided a common ground.

However, even so, there are some American researchers who claim that even though most people think of themselves as "middle class", there really is a significant class structure in the U.S. too and that it needs to be better studied:
http://www.nytimes.com/pages/national/class/

Whether you want to consider their definitions of "class" as being the same, will affect how you answer your question. There is no doubt, however, that the divisions they note are real and significant.

Answer 2

it is the MOST relevant concept. ( although it's not a "concept") it colors the way people act and think on the most important issues facing humanity, i.e. poverty, hunger, disease, peace of mind, climate change, human rights, etc. and it will soon reach critical mass......