Please take a look at https://github.com/dangrossman/bootstrap-daterangepicker

It would be nice to have similar option in DatePicker - to choose range of days.

It would be great if we can have the option to have a multi-month view calendar.  Like the one in the asp.net ajax suite.
 
http://demos.telerik.com/aspnet-ajax/calendar/examples/functionality/multimonthview/defaultcs.aspx

Provide properties to set min/max time of the DateTimePicker, e.g always shows from 8AM to 5PM of everyday.

Add a multiple date selection to the Calendar. A multiple date selection calendar is very important for professional web applications in many situations. Also, there is a lack of events in the API.
It is always important to provide more events then less.

Here a few suggestions:
Property year;    /// Year displayed by control.
Property month; /// Month (1 to 12) displayed by control.
A method in the API to easily get the selected date(s).
A method in the API to easily set the selected date(s).
An option to indicate if we allow/disallow multi-selection.
A callback event (and passing the data as an argument) when a date is selected/unselected to allow/disallow the selection/deselection (by returning a true/false). This would allow to easy show a warning message when some dates are selected/unselected. We may currently do part of it in the change event but adding events onbefore/onafter selection would be nice.
Add the option to hide/show days from previous/next month.
Add the option to enabled/disable click from previous/next month.
The Year selection on the top should be a combo that allow keyboard input.
You may check the Yahoo Calendar event & properties. It will provide a good examples (http://developer.yahoo.com/yui/docs/YAHOO.widget.Calendar.html)

Many calendars have the ability to show a column of ISO week numbers alongside the dates (either to the right or the left).  Although it's not a show stopper I have such a requirement in my current project.  While other controls offer this there are none I know of which permit custom calculation of the week number - another requirement for this project.