De-Nesting Lists

Sed, 20 chars

Solution is based on POSIX Extended Regular Expression.

s;[^0-9]+0|[],[]+;;g

Output:

bash-3.2$ sed -rf sedFile <<< "[[[4, 5, 8]], [[5, 6, 20]], [[1, 20, 500]]]" 
4 5 8 5 6 20 1 20 500

Edit: POSIX Basic Regular Expression(@clueless's solution), 19 chars:

s/[^0-9][^1-9]*/ /g

0~⍨⍎⍞~'[]'

Explanation:

⍞~'[]': User input (⍞) without (~) the characters '[]'
This gives something like '1,2,0,2,3'
⍎: Evaluate this string. It so happens that , is the concatenation operator, so now we have a list: 1 2 0 2 3 (APL lists are whitespace-separated by default)
0~⍨: Remove all the numbers 0 from this list. (It is a list of numbers, not of strings, by now, so zeroes within numbers are not removed.
This value is output (by default, because it's the value of the whole program, kind of like Golfscript). APL lists are whitespace-separated by default so it looks exactly like in the question.

def d(x):
 try:map(d,x)
 except:print`x`*(x!=0)