Linux can be used on some devices at the primary bootloader. The size requirements on the first-stage bootloader are more stringent than for the ultimate running operating system.

There are projects along these lines, such as the coreboot project, or petitboot

• want a small flash and ram footprint (how small?)
• depending on the platform, may need to read the "main" filesystem of the machine
• faster booting than other bootloaders
• re-use of Linux device drivers

There is currently a migration from 8-bit micro-controllers to 32-bit micro-controllers in the deeply embedded space. These types of processors are used in industrial automation, sensors, infrastructure, and more… Some of these devices may need to be powered for a long time on a coin cell battery, or be powered by ambient energy.

• ultra low-power solutions need to avoid DRAM completely. This usually means that the entire system should fit entirely in on-chip static RAM. Current size for this could be 256K or 512K

emcraft makes boards with these types of processors

Also, see this article about using uClinux on Cortex-M3 devices: Practical Advice on Running uClinux on Cortex-M3/M4

A program may want to run at high performance entirely within the L2 cache of the processor it is on. If the combination of kernel and program is small enough, it can avoid accessing main memory entirely.

Here are some chips with on-chip memory that could run Linux with no external RAM:

• http://linuxgizmos.com/quad-core-cortex-a15-soc-features-6mb-on-chip-ram/ TI quad-core ARM chip with 6 MB on-chip RAM
• Intel Quark - http://en.wikipedia.org/wiki/Intel_Quark (512KB on-board SRAM)