Remove leading zero in Java

1. Stop reinventing the wheel. Almost no software development problem you ever encounter will be the first time it has been encountered; instead, it will only be the first time you encounter it.
2. Almost every utility method you will ever need has already been written by the Apache project and/or the guava project (or some similar that I have not encountered).
3. Read the Apache StringUtils JavaDoc page. This utility is likely to already provide every string manipulation functionality you will ever need.

Some example code to solve your problem:

public String stripLeadingZeros(final String data)
{
    final String strippedData;

    strippedData = StringUtils.stripStart(data, "0");

    return StringUtils.defaultString(strippedData, "0");
}

If the string always contains a valid integer the return new Integer(value).toString(); is the easiest.

public static String removeLeadingZeroes(String value) {
     return new Integer(value).toString();
}

You could add a check on the string's length:

public static String removeLeadingZeroes(String value) {
     while (value.length() > 1 && value.indexOf("0")==0)
         value = value.substring(1);
         return value;
}

I would consider checking for that case first. Loop through the string character by character checking for a non "0" character. If you see a non "0" character use the process you have. If you don't, return "0". Here's how I would do it (untested, but close)

boolean allZero = true;
for (int i=0;i<value.length() && allZero;i++)
{
    if (value.charAt(i)!='0')
        allZero = false;
}
if (allZero)
    return "0"
...The code you already have