* For DOB, what you typically need looks more like three text boxes. That said, the text boxes need to be able to work together in terms of validation - the 31st of February 2015 is not a valid date! This is why it's better to think of this as a single form control with multiple input fields. Alternatively, I want something where I can pick the year first, but this typically leads to lots of scrolling.
* For adding an appointment, I probably want something closest to the conventional date picker, but even then, if I'm making an appointment for a group, I might still want additional information about when people are available displayed directly in the calendar view as I'm choosing a date.
* If I want to browse for the cheapest date, then I want a way of seeing all the dates available and the prices of those dates at the same time, meaning a relatively rich date picker control. If all I have is "next day"/"previous day", then I need to manually click around a lot to get good deals.
* If I want to select a range of dates, then I want a single control that allows me to select that range immediately, not having to open a "start" field and an "end" field separately. I also probably want multiple months visible, depending on how long my range is, so I can see the whole range at a glance without having to click back and forth between months.
* This is more subtle, but a hotel visit requires a range of dates, but a flight to and from the hotel requires two discrete dates, which might potentially be indicated with yet another date picker variant.
These are all flows that require me to pick a date, most of them from a calendar, and all of them could arguably be considered important enough for a native element (in the sense that I use all of these elements in my day-to-day web browsing). But they're all very different, require different interactions and content, and have subtly different purposes.
