Write a program which replaces with spaces the braces in cases where braces in places cause stasis

Ruby, 223 characters

This one turned out a bit long.

u,b,i=[],[[],[],[]],-1
s=gets.gsub(/(\/\*|"|').*?(\*\/|"|')|~/){|m|u+=[m];?~}
s.chars{|c|i+=1
(t='{[('.index(c))?b[t].push(i):((t='}])'.index(c))&&(b[t].pop||s[i]=' '))}
b.flatten.map{|l|s[l]=' '}
puts s.gsub(/~/){u.shift}

What it does is take out the strings and comments first, so they don't get counted (and puts them back in later).

Then, it goes through the string character by character. When it finds an opening brace, it stores its position. When it finds a closing brace, it pops from its respective open brace storage array.

If pop returns nil (i.e. there weren't enough opening braces), it removes the closing brace. After this entire thing is done, it removes the remaining extra opening braces (i.e. there weren't enough closing braces).

At the end of the program, it puts all the strings and comments back and outputs them.

Ungolfed:

in_str = gets

# grab strings and comments before doing the replacements
i, unparsed = 0, []
in_str.gsub!(/(\/\*|"|').*?(\*\/|"|')|\d/){|match| unparsed.push match; i += 1 }

# replaces with spaces the braces in cases where braces in places cause stasis
brace_locations = [[], [], []]
in_str.each_char.with_index do |chr, idx|
    if brace_type = '{[('.index(chr)
        brace_locations[brace_type].push idx
    elsif brace_type = '}])'.index(chr)
        if brace_locations[brace_type].length == 0
            in_str[idx] = ' '
        else
            brace_locations[brace_type].pop
        end
    end
end
brace_locations.flatten.each{|brace_location| in_str[brace_location] = ' ' }

# put the strings and comments back and print
in_str.gsub!(/\d+/){|num| unparsed[num.to_i - 1] }
puts in_str

Python 3, 410 322 317

import re;a='([{';z=')]}';q=[re.findall('".*?"|/\*.*?\*/|.',input())]
while q:
 t=q.pop(0);s=[];i=0
 for x in t:
  if x in a:s+=[x]
  try:x in z and 1/(a[z.find(x)]==s.pop())
  except:s=0;break
 if[]==s:print(''.join(t));break
 while 1:
  try:
   while t[i]not in a+z:i+=1
  except:break
  u=t[:];u[i]=' ';q+=[u];i+=1

Tries every possible set of deletions, starting with smaller ones, until it finds one where the braces are balanced. (By which I mean fully correctly balanced: {{(}) produces ( ), not {(}).)

The first version used a recursive generator function, which was really cool but also really long. This version performs a simple breadth-first search using a queue. (Yes, it's a factorial time algorithm. What's the problem? :^D)

C - 406

An Attempt in C without using regular expressions.

#define A if((d==125||d==93||d==41)
char*s;t[256];f(i,m,n,p){while(s[i]!=0){int c=s[i],k=s[i+1],v=1,d;if((c==42&&k==47)||(c==m&&i>n))return i;if(!p||p==2){if((c==39||c==34)||(c==47&&k==42)){i=f(i,c*(c!=47),i,p+1);
c=c==47?42:c;}d=c+1+1*(c>50);A){v=f(i+1,d,i,2);if(!p&&v)t[d]++;if(p==2&&v)i=v;}}d=c;A&&!p){v=!!t[c];t[c]-=v;}if(p<2)putchar(c*!!v+32*!v);i++;}return 0;}main(int c,char*v[]){s=v[1];f(0,0,0,0);}

To compile and run (on a linux machine):
gcc -o brackets brackets.c
./brackets "[(])"

In undefined cases like [ ( ] ) it returns the last valid bracket pair ( )