What's so great about ARM?
Performance is one advantage. Being a 32-bit processor it outperforms (almost) all 8-bit controllers DMIPS-wise. The core also has gone through several generations, read optimizations.
These optimizations not only show in performance numbers, but in power consumption as well. The most recent core has doubled its DMIPS/mW ratio compared to the previous generation (see also this answer).
ARM is available from a great many manufacturers, more than any other microcontroller, and each has a number of versions to choose from, with different combinations of on-chip peripherals and memory, and packages. Case in point: NXP offers no less than 35 controllers with on-chip Ethernet.
ARMs are inexpensive; ARM was probably the first 32-bit controller to break the USD 1 barrier.  

This combination of performance, wide offering and low cost make it such that you simply can't ignore ARM:


  In 2005 about 98 percent of all mobile phones use at least one ARM-designed core on their motherboards, according to research from the analyst firm the Linley Group. (source) 


The mobile phone market has also another effect. Mobile phones are very space constrained and demand small packages. NXP's LPC1102 comes in a WLP-16 package just 5mm\$^2\$, a scale previously only used by low pin-count 8-bit microcontrollers.