Re: other options & considerations...
For dates like airline or hotel reservations (usually later in the current year) I personally prefer the simultaneous ability to enter text or choose from a pop-up calendar. For a web-app there are jQuery plugins that can accomplish this pretty nicely, or just use the native datePicker control, which people understand & can use fairly easily.
Another potential hiccup to consider regardless of device: localization of date formats.
What month names, calendar systems, or non-Latin alphabets might you need to consider based on your users?
Using "DD/MM/YYYY" works fine for most European countries, but can be confusing in the US where (for some unknown reason) people often write dates as MM/DD/YYYY.
For example, in Japan these are the same date, and are reversed from the European standard:
昭和６０ １０月１２日 (GGYY/MM/DD, where "G" is the Imperial era for counting years)
Sure, most people would probably understand a clearly labeled input field, but it may be worth considering depending on your target audience.
For a native mobile app, the OS can usually assist with formatting the info to fit the user's chosen device settings. For a web-app, perhaps consider something like Moment.js or a PHP solution rather than hard-coding a single option into an input field. Handling different formats would likely require separate fields so they can be manipulated independently (although you could likely parse a single-line input into a standard format, it's more prone to typos & variations even within a given locale).