I've heard the use of serial interfaces of router is not so common in the current network environment. But in some exams like CCNA, you can still see questions including the knowledge of serial interface. So, I don't know if it is true or not that using serial interfaces is not common.
As Ricky Beam has already written, even though Serial connections might not be common where you live, that doesn't mean they don't exist.
Over 90% of the connections we have in Europe use either Ethernet or xDSL. But in countries like Philippines, Nigeria and Cameroon, we have a lot of Serial connections.
In the end i guess it depends a lot upon where you are and what is available, that is also why Cisco have not ruled this type of connection out of their certifications. I do not know of any database specifying the most used connections based on which country you are located.
Long distance Ethernet has grown massively in popularity, because it is cheap, and because it means you don't have to deal with two different technologies for LAN and WAN.
However, building physical infrastructure has both significant economies of scale and significant regulatory implications. So, except for very short distances, it's rarely economical to do it yourself.
What that means is you ultimately have to deal with what the local communications provider(s) will sell you at a price you can afford. If the local communications network is still using oldschool telco equipment and standards then you will have to deal with that.