ARM already has a lot of deployed CPUs in many mobile devices, particularly PDAs, but doesn't have CPUs in more advanced devices like ultra-portables or laptops. Intel does, and ARM would face an uphill battle if trying to squeeze into the laptop market. Intel is definitely making it clear that they feel the Atom is a better choice in the future than existing CPUs that companies like ARM and TI make. ARM's newer CPU is soon to get a technical refresh, one that will enable an embedded CPU to boast four cores. What would you do with four cores in a cell phone? ARM seems to think that as devices like the iPhone mature, they will have more justification for such a device.
TI is not preparing to directly take on Intel as is ARM, but does plan to use ARM cpus in upcoming platforms.