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BAK by Prfnoff

A language that relies on self-reference, though I can't remember how it works.  Its filename extension, .BAK, was chosen specially to cause confusion with the backup files that some of the more traditional editors automatically create.

Befunge by Chris Pressey

A two-dimensional language in which the program counter can move in any of the four main compass directions.  Each instruction is represented by a single character, and the instruction set is based on a stack-based machine.  The language has no built-in distinction between code space and data space, and so programs can be self-modifying.

The original version, Befunge-93, has as its program space an 80 × 25 torus.  Later versions, Befunge-96, Befunge-97 and Funge-98, generalise this to an unbounded Lahey space.

See also: Apple Befunge

Quines in Befunge

Blank by Andrew Turley

A one-dimensional fungeoid in which program flow can go in either direction through a ring of instructions.

Brainf*** by Urban Müller

(Sometimes two or more of the asterisks in the name are censored out with letters.)

A Turing tarpit of eight parameterless instructions, designed as a tiny language for which the world's smallest compiler could be produced.

Along with Shelta, it is one of the few esoteric languages that has been bootstrapped, i.e. a Brainf*** compiler has been written in Brainf***.

See also: Doublef***

Brainfork by Asger Ipsen

An extension of Brainf*** with an extra instruction to support multithreading.

Bub

Brainf*** Ugly Bodge.  An adaptation of Brainf*** to be even easier to interpret than Brainf*** already is.  It is straightforward to translate any Brainf*** program into Bub.

Bullfrog by Ryan Kusnery

Has no conditionals or loops; all control flow must be done using computed jumps.

Byte Syze by Stewart Gordon

A simple language in which everything is a byte in syze.