All dates between two Date objects (Swift)

Just add one day unit to the date until it reaches
the current date (Swift 2 code):

var date = startDateNSDate // first date
let endDate = NSDate() // last date

// Formatter for printing the date, adjust it according to your needs:
let fmt = NSDateFormatter()
fmt.dateFormat = "dd/MM/yyyy"

// While date <= endDate ...
while date.compare(endDate) != .OrderedDescending {
    print(fmt.stringFromDate(date))
    // Advance by one day:
    date = calendar.dateByAddingUnit(.Day, value: 1, toDate: date, options: [])!
}

Update for Swift 3:

var date = startDate // first date
let endDate = Date() // last date

// Formatter for printing the date, adjust it according to your needs:
let fmt = DateFormatter()
fmt.dateFormat = "dd/MM/yyyy"

while date <= endDate {
    print(fmt.string(from: date))
    date = Calendar.current.date(byAdding: .day, value: 1, to: date)!
}