bperrybap:
I think looking at google trends is a good indication about somethings popularity or relevance.
Here is BASCOM vs Arduino:
http://www.google.com/trends/explore#q=bascom%2C%20Arduino&cmpt=q
World wide Google searches for BASCOM (not just BASCOM AVR) is waining while searches for Arduino is still climbing quite rapidly.
You compare Bascom, a software tool, an IDE, with Arduino which is an IDE and also a series of boards.
A more fair comparison would be:
Bascom AVR
Arduino IDE
see: http://www.google.com/trends/explore#q=Bascom%20AVR%2C%20Arduino%20IDE&cmpt=q
The interest in "Arduino IDE" has increased in the last four years and now in December 2012 it is roughly the same as in "Bascom AVR". We have to wait and see what happens in the future.