Google did worldwide research on just that topic and published the results on their Analytics blog.  It appears that yes, the web is indeed getting faster with the largest improvements in speed coming on the mobile platform. 
The study gathered the speed of “opted-in publishers” around the world for one week.  This year’s data (2013) was compared to last year’s and here’s what they found:  page load times decreased slightly in 2013 (meaning they loaded faster), but web pages on mobile devices loaded 30% faster than they did in 2012.

These increased speeds are even more impressive when you consider that web page size increased by 56% over the same period.

Google gives credit for the increased speeds to faster web browsers, faster networks as well as the mobile devices themselves processing data at increasingly faster speeds.

So which countries web pages’ load the fastest?

For desktop in 2012 it was Japan; in 2013 Sweden.  The top five in 2013 (from 1 to 5) are Sweden and Japan, with Canada, the U.S. and the Russian Federation in a virtual tie for third.

On the mobile platform, the top five for 2013 are (from 1 to 5):  U.S., Germany, Japan, Sweden and the U.K.