There are lots of different conventions for writing dates, depending on the country.This wiki article provides a useful summary. As long as it's not ambiguous then most people can work it out regardless of what format you use. 4/9/2015 is ambiguous, because both 4 and 9 can be a month, but 13/9/2015 is unambiguous because 13 cannot be a month.
Generally, it is preferable not to use digits in text: "that's the second time you broke the photocopier!" rather than "...the 2nd time...". With dates, there are too many numbers to write nineteen hundred and ninety five, so we use digits for the day and year, but generally we write month names in full, rather than abbreviated or in digits.
Note that, for some dates that have a special significance, we generally write the day in full: "the fourth of July" (independence day in America), "the first of April" (April fool's day), "the fifth of November" (bonfire night in the UK).