Here is an attempt, with the caveat that your example is really complicated, and that you haven't really defined what the JSON result should look like:

#!/usr/bin/perl

use strict;
use warnings;

use Bio::Phylo::IO;
use JSON;

my $forest=Bio::Phylo::IO->parse(-file=>"example.newick", -format=>"newick");

while (my $tree=$forest->next) {
    my $out=[];
    my $children=$out;
    my $cur;
    my $parent;
    $tree->visit_breadth_first(
                               -pre=>sub { $cur={ name=>shift->get_name }; push @$children, $cur; },
                               -pre_daughter=>sub { $cur->{children}=[]; $parent=$cur; $children=$cur->{children} },
                              );
    print JSON->new->pretty->encode($out);
}

If I run it on a smaller example (from wikipedia's entry on Newick format):

(A,B,(C,D)E)F;

I get this:

[
   {
      "name" : "F",
      "children" : [
         {
            "name" : "A"
         },
         {
            "name" : "B"
         },
         {
            "name" : "E",
            "children" : [
               {
                  "name" : "C"
               },
               {
                  "name" : "D"
               }
            ]
         }
      ]
   }
]

But again, I don't know how you want the JSON output formatted.

What's great about using python to output JSON is that stringifying native python arrays/dictionary conforms to JSON specs. So you can really just print str(myStructure) and it will output JSON accordingly.

Like I said previously, I am not sure how you want the JSON to look as there are no standardized rules for writing Newick in JSON. I just made it output a simple key:value structure. For example the output of your sample would be something like: (I took out a bunch of data in the middle so I don't go over the post character limit)

{'Opisthokonta': ['Capsasporaowczarzaki', {'Codonosigidae': ['Proterospongia', 'Monosigabrevicollis']}, {'Metazoa': .....[bunch of stuff]}, {'Fungi': ['  Spizellomycespunctatus', 'Allomycesmacrogynus', 'Saccharomycescerevisiae', 'Phycomyces_blakesleeanus']}]}

Here is something in python without using BioPython (yes I was bored):

edit** This is just for fun. Use the BioPython/BioPerl solutions from the other answers if you want accurate results.

Not sure if it's 100% working with everything; however, It does work with your sample. It requires a root node.

def parseNode(nwString):
    parenCount = 0

    key = ''
    processed = ''
    index = 0
    for char in nwString:
        if char == "(":
            parenCount += 1
            if parenCount == 1:
                continue
        elif char == ")":
            parenCount -= 1
            if parenCount == 0:
                if index + 2 > len(nwString):
                    break
                else:
                    key = nwString[index + 2:]
                    break

        if char == ",":
            if parenCount != 1:
                processed += "|"
            else:
                processed += ","
        else:
            processed += char

        index += 1

    data = processed.split(',')

    for i in range(len(data)):
        data[i] = data[i].replace('|',',')

    return (key.strip(),data)

def recurseBuild(nwString):
    if nwString.find('(') == -1:
        if len(nwString.split(',')) == 1:
            return nwString
        else:
            return nwString.split(',')
    else:
        key, data = parseNode(nwString)

        dataArray = []
        for item in data:
            dataArray.append(recurseBuild(item))

        return {key:dataArray}

result = recurseBuild(myNewickstring)

print result

Here is a C lex/yacc solution: https://gist.github.com/3056165

The bison parser: https://raw.github.com/gist/3056165/54220d50bcad1a72462bdb00dc258d6d472c7cfd/newick.y

The *flex lexer: https://raw.github.com/gist/3056165/407f2924a533793b33c9c5b0d144ca7e1dd24e31/newick.l

The Makefile:

all:
bison -d newick.y
flex newick.l
gcc -Wall -O3 newick.tab.c lex.yy.c

Test:

a.out < input.newick.txt | fold -w 60

{"label":"Opisthokonta","children":[{"label":"Capsasporaowcz
arzaki"},{"label":"Codonosigidae","children":[{"label":"Prot
erospongia"},{"label":"Monosigabrevicollis"}]},{"label":"Met
azoa","children":[{"label":"Amphimedonqueenslandica"},{"labe
l":"Trichoplaxadhaerens"},{"label":"Eumetazoa","children":[{
"label":"Bilateria","children":[{"label":"Coelomata","childr
en":[{"label":"Deuterostomia","children":[{"label":"Chordata
(...)
[{"label":"Caenorhabditisjaponica"},{"label":"Caenorhabditis
brenneri"},{"label":"Caenorhabditisremanei"},{"label":"Caeno
rhabditiselegans"},{"label":"Caenorhabditisbriggsae"}]}]},{"
label":"Schistosomamansoni"}]},{"label":"Cnidaria","children
":[{"label":"Nematostellavectensis"},{"label":"Hydramagnipap
illata"}]}]}]},{"label":"Fungi","children":[{"label":"Spizel
lomycespunctatus"},{"label":"Allomycesmacrogynus"},{"label":
"Saccharomycescerevisiae"},{"label":"Phycomyces_blakesleeanu
s"}]}]}

Speed ?

$ time (x=1; while [ $x -le 1000 ]; do  ./a.out < input.newick.txt > /dev/null ; x=$(( $x + 1)); done )

real    0m2.876s
user    0m0.192s
sys    0m0.516s