They vary from formal to informal, and there are differences between British and American English.
The following table shows some typical formats:
|FORMAT||BRITISH: DAY-MONTH-YEAR||AMERICAN: MONTH-DAY-YEAR|
|A||The Fifth of January, 2016||January the Fifth, 2016|
|B||5th January 2016||January 5th, 2016|
|C||05 January 2016||January 05, 2016|
The format to use is a question of formality, politeness and personal choice.
Generally, the longer formats, such as B or C, are more polite (since they show more respect for the reader).
Shorter formats, such as D, are used in less formal situations, for example a memo, a letter between friends or an impersonal business letter.
Format A is extremely formal and mainly used on printed items, for example a wedding invitation.
The numerical formats may use a full stop (.) or a hyphen (-) instead of a slash (/), for example: 05.1.2016 or 01-05-16.