Get day of week using NSDate

What you are looking for (if I understand the question correctly) is NSCalendarUnit.CalendarUnitWeekday. The corresponding property of NSDateComponents is weekday.

Note also that your date format is wrong (the full specification can be found here: http://unicode.org/reports/tr35/tr35-6.html).

The function can be simplified slightly, using automatic type inference, also you use variables a lot where constants are sufficient. In addition, the function should return an optional which is nil for an invalid input string.

Updated code for Swift 3 and later:

func getDayOfWeek(_ today:String) -> Int? {
    let formatter  = DateFormatter()
    formatter.dateFormat = "yyyy-MM-dd"
    guard let todayDate = formatter.date(from: today) else { return nil }
    let myCalendar = Calendar(identifier: .gregorian)
    let weekDay = myCalendar.component(.weekday, from: todayDate)
    return weekDay
}

Example:

if let weekday = getDayOfWeek("2014-08-27") {
    print(weekday)
} else {
    print("bad input")
}

Original answer for Swift 2:

func getDayOfWeek(today:String)->Int? {

    let formatter  = NSDateFormatter()
    formatter.dateFormat = "yyyy-MM-dd"
    if let todayDate = formatter.dateFromString(today) {
        let myCalendar = NSCalendar(calendarIdentifier: NSCalendarIdentifierGregorian)!
        let myComponents = myCalendar.components(.Weekday, fromDate: todayDate)
        let weekDay = myComponents.weekday
        return weekDay
    } else {
        return nil
    }
}

Swift 3 & 4

Retrieving the day of the week's number is dramatically simplified in Swift 3 because DateComponents is no longer optional. Here it is as an extension:

extension Date {
    func dayNumberOfWeek() -> Int? {
        return Calendar.current.dateComponents([.weekday], from: self).weekday 
    }
}

// returns an integer from 1 - 7, with 1 being Sunday and 7 being Saturday
print(Date().dayNumberOfWeek()!) // 4

If you were looking for the written, localized version of the day of week:

extension Date {
    func dayOfWeek() -> String? {
        let dateFormatter = DateFormatter()
        dateFormatter.dateFormat = "EEEE"
        return dateFormatter.string(from: self).capitalized 
        // or use capitalized(with: locale) if you want
    }
}

print(Date().dayOfWeek()!) // Wednesday