How to convert String to Date without knowing the format?

You cant!

If you have the date 2010-08-05 then it can be either 5th August 2010, or 8th May 2010 - you need to know the date format (or at least prioritise one format over the over) to tell them apart.

I agree with Kragen that in the general case there is no correct solution. However, if the following conditions hold, you may use the solution below:

1. You have a set of all possible formats

2. There is no ambiguity between the formats; no date expression can be successfully parsed by two of them.

Consider the following solution which iterates over a list of possible formats. This solution makes use of ThreadLocal, in order to make date parsing efficient in a multi-threaded environment (remember that SimpleDateFormat isn't thread safe):

public class FlexibleDateParser {
    private List<ThreadLocal<SimpleDateFormat>> threadLocals = new  ArrayList<ThreadLocal<SimpleDateFormat>>();

    public FlexibleDateParser(List<String> formats, final TimeZone tz){
        threadLocals.clear();
        for (final String format : formats) {
            ThreadLocal<SimpleDateFormat> dateFormatTL = new ThreadLocal<SimpleDateFormat>() {
                protected SimpleDateFormat initialValue() {
                    SimpleDateFormat sdf = new SimpleDateFormat(format);
                    sdf.setTimeZone(tz); 
                    sdf.setLenient(false);
                    return sdf;
                }
            };
            threadLocals.add(dateFormatTL);
        }       
    }

    public Date parseDate(String dateStr) throws ParseException {
        for (ThreadLocal<SimpleDateFormat> tl : threadLocals) {
            SimpleDateFormat sdf = tl.get();
            try {
                return sdf.parse(dateStr);
            } catch (ParseException e) {
                // Ignore and try next date parser
            }
        }
        // All parsers failed
        return null;
    }       
}

As noted before, you need to at least have an ordered list of pattern candidates. Once you have that, Apache DateUtils has a parseDate(String dateString, String[] patterns) method that lets you easily try out a list of patterns on your date string, and parse it by the first one that matches:

public static Date parseDate(String str,
                         String[] parsePatterns)
                  throws ParseException

Parses a string representing a date by trying a variety of different parsers.

The parse will try each parse pattern in turn. A parse is only deemed successful if it parses the whole of the input string. If no parse patterns match, a ParseException is thrown.

The parser will be lenient toward the parsed date.

Here is a quick and dirty solution based on american date formats.

public Date parseDate(String strDate) throws Exception
{
    if (strDate != null && !strDate.isEmpty())
    {
        SimpleDateFormat[] formats =
                new SimpleDateFormat[] {new SimpleDateFormat("MM-dd-yyyy"), new SimpleDateFormat("yyyyMMdd"),
                        new SimpleDateFormat("MM/dd/yyyy")};

        Date parsedDate = null;

        for (int i = 0; i < formats.length; i++)
        {
            try
            {
                parsedDate = formats[i].parse(strDate);
                return parsedDate;
            }
            catch (ParseException e)
            {
                continue;
            }
        }
    }
    throw new Exception("Unknown date format: '" + strDate + "'");
}

Your problem is related to Internationalization. As Kragen answered, you can't just parse date in unknown format. Although you can scan all possible locales and parse something, but you wouldn't know if it was parsed correctly.

Just a little i18n background:

Q: Can you tell me what day month and year this date is referring to:

09/11/10?

A: Without knowing the locale, you can't. It could be anything. September, 11th in USA. November, 9th in Great Britain. And so on.