Swift (3.x) version of two most popular solutions in form of Date extension :
extension Date {
    static var is24HoursFormat_1 : Bool  {
        let dateString = Date.localFormatter.string(from: Date())
        if dateString.contains(Date.localFormatter.amSymbol) || dateString.contains(Date.localFormatter.pmSymbol) {
            return false
        }
        return true
    }
    static var is24HoursFormat_2 : Bool {
        let format = DateFormatter.dateFormat(fromTemplate: "j", options: 0, locale: Locale.autoupdatingCurrent)
        return !format!.contains("a")
    }
    private static let localFormatter : DateFormatter = {
        let formatter = DateFormatter()
        formatter.locale    = Locale.autoupdatingCurrent
        formatter.timeStyle = .short
        formatter.dateStyle = .none
        return formatter
    }()
}
Usage :
Date.is24HoursFormat_1
Date.is24HoursFormat_2
Swift (2.0) version of two most popular solutions in form of NSDate extension :
extension NSDate {
    class var is24HoursFormat_1 : Bool  {
        let dateString = NSDate.localFormatter.stringFromDate(NSDate())
        if dateString.containsString(NSDate.localFormatter.AMSymbol) || dateString.containsString(NSDate.localFormatter.PMSymbol) {
            return false
        }
        return true
    }
    class var is24HoursFormat_2 : Bool {
        let format = NSDateFormatter.dateFormatFromTemplate("j", options: 0, locale: NSLocale.autoupdatingCurrentLocale())
        return !format!.containsString("a")
    }
    private static let localFormatter : NSDateFormatter = {
        let formatter = NSDateFormatter()
        formatter.locale    = NSLocale.autoupdatingCurrentLocale()
        formatter.timeStyle = .ShortStyle
        formatter.dateStyle = .NoStyle
        return formatter
    }()
}
Please note that Apple says following on NSDateFormatter (Date Formatters) : 
Creating a date formatter is not a cheap operation. If you are likely
  to use a formatter frequently, it is typically more efficient to cache
  a single instance than to create and dispose of multiple instances.
  One approach is to use a static variable.
Thats the reason for static let 
Secondly you should use NSLocale.autoupdatingCurrentLocale() ( for is24HoursFormat_1 ), that way you will always get the actual current state.