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)!
}

Using extension:

extension Date {
    static func dates(from fromDate: Date, to toDate: Date) -> [Date] {
        var dates: [Date] = []
        var date = fromDate
        
        while date <= toDate {
            dates.append(date)
            guard let newDate = Calendar.current.date(byAdding: .day, value: 1, to: date) else { break }
            date = newDate
        }
        return dates
    }
}

Usage:

let datesBetweenArray = Date.dates(from: Date(), to: Date())