One major thing that the others have left out is dealing with the timezone (TZ). Anytime you use a SimpleDateFormat to go to/from a string representation of the date, you really need to be aware of what TZ you're dealing with. Unless you explicitly set the TZ on the SimpleDateFormat, it will use the default TZ when formatting/parsing. Unless you only deal with date strings in the default timezone, you'll run into problems.
Your input date is representing a date in GMT. Assuming that you also want the output to be formatted as GMT, you need to make sure to set the TZ on the SimpleDateFormat:
public static void main(String[] args) throws Exception
{
String inputDate = "Tue Mar 19 00:41:00 GMT 2013";
// Initialize with format of input
SimpleDateFormat sdf = new SimpleDateFormat("EEE MMM dd HH:mm:ss z yyyy");
// Configure the TZ on the date formatter. Not sure why it doesn't get set
// automatically when parsing the date since the input includes the TZ name,
// but it doesn't. One of many reasons to use Joda instead
sdf.setTimeZone(TimeZone.getTimeZone("GMT"));
Date date = sdf.parse(inputDate);
// re-initialize the pattern with format of desired output. Alternatively,
// you could use a new SimpleDateFormat instance as long as you set the TZ
// correctly
sdf.applyPattern("yyyy-MM-dd HH:mm:ss");
System.out.println(sdf.format(date));
}