Hexadecimal Counter

Pure Bash, 26

Counts from 0x0 to 0x3F:

echo {0..3}{{0..9},{A..F}}

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CJam, 21 14 bytes

A,_6,'Af++m*S*

Prints the numbers 00 to 9F.

Try it online in the CJam interpreter.

How it works

A,             e# Push [0 ... 9].
  _            e# Push a copy.
   6,          e# Push [0 ... 5].
     'Af+      e# Add 'A' to each. This pushes "ABCDEF".
         +     e# Concatenate. This pushes [0 ... 9 'A' ... 'F'].
          m*   e# Cartesian product. This pushes [[0 0] ... [9 'F'].
            S* e# Join, separating by spaces.

Python 2, 52

a=0
for b in'0123456789ABCDEF'*4:print`a`+b;a+=b>'E'

Prints 00 to 3F. Takes advantage of the fact that the first digit a is always a number in this range. Loops through four cycles of the second digit b, incrementing a whenever the second digit is F.

This is one char shorter than the more direct

for a in'0123':
 for b in'0123456789ABCDEF':print a+b