A family of CPUs made by Motorola, sometimes also referred to as "68k".
It has 16 32-bit registers, split into 8 data and 8 address registers. The instruction set is quite orthogonal and instructions are always multiples of 16 bits in length. Accesses to anything larger than a byte have to be 16-bit aligned. Overall, the architecture has a strong RISC feel to it, though it is not. The architecture has always been fully 32-bit, as opposed to the x86 design, which started out as a 16-bit design that was painfully evolved to 32-bit.
The 68000, the first in the series, was introduced in September 1979, and only had a 24-bit address bus. The 68010, introduced in 1982, allowed the use of VirtualMemory, but offered too little additional further advantages to justify its price in the eyes of most customers. The 68020, debuting in 1984, was fully 32-bit, and software could take immediately advantage of this because the architecture had always been designed for the fact. The 68k family enjoyed wide deployment, and is nowadays still used in embedded devices. Some architectures built around this CPU family include:
The original 68000 design was in production by Motorola up until 2000, and is still in production under license by others, along with its successors and many licensed derivative designs of all the designs of the family. Innumerable devices employ these CPUs even today.
You can run Linux on a range of 680x0-based systems thanks to the effort of the Linux/m68k project. Ports exist to a variety of systems; f.ex., on later AppleMacintoshes that use the 68030 and upwards (such as the SE30), its Linux/mac68k subproject allows running Debian. See the Linux/m68k project for more architectures.
7 pages link to 680x0: