Shortest auto-destructive loop

Python, 16 bytes

The non-interesting 0 division approach:

for x in 1,0:x/x

The first iteration computes 1 / 1, which works fine. The second iteration tries to compute 0 / 0, resulting in a ZeroDivisionError being thrown.

17 bytes (personal favourite)

i=1
while i:del i

Initially, i=1 which is truthy, so the loop is entered.

The first time the loop is run, the variable i is deleted.

This means that, the second time, i is no longer a variable and therefore its evaluation fails with NameError: name 'i' is not defined.

---

Another 15 byte solution would be def _():_() (newline) _(), because Python does not optimize tail recursion. However, this violates rule #6.

MATL, 5 1 byte

Idea taken from @MartinEnder's CJam answer

`

Try it online!

`    % Do...while loop
     % Implicit end. The loop continues if the top of the stack is true.
     % After the first iteration, since the stack is empty, the program 
     % implicitly tries to take some non-existing input, and finishes
     % with an error

---

Old version

2:t"x

Try it online!

2:   % Push [1 2]
t    % Duplicate
"    % For each (i.e. do the following twice)
  x  %   Delete top of the stack. Works the first time. The second it tries to
     %   implicitly take some non-existing input, and finishes with an error

Jelly, 3 2 bytes

Ṿß

Kills itself by running out of memory. Locally does so after ~100 seconds.

Try it online! (death certificate in Debug drawer)

How it works

Ṿß  Main link. Argument: x. Implicit first argument: 0

Ṿ   Uneval; yield a string representation of x.
 ß  Recursively call the main link.
    Jelly uses TCO, so the first cycle finishes successfully before entering
    the next one.

The first few iterations yield:

'0'
'”0'
'””,”0'
'””,””,”,,””,”0'
'””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,”0'
'””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,”,,”,,””,”,,”,,””,””,”,,””,””,”,,””,”,,”,,””,””,”,,””,”0'

After that, it gets real ugly, real fast.