在Swift 2.1.1和xcode 7.1 OSX 10.10.5中，你可以使用函数添加任意数量的天数

func addDaystoGivenDate(baseDate:NSDate,NumberOfDaysToAdd:Int)->NSDate
{
    let dateComponents = NSDateComponents()
    let CurrentCalendar = NSCalendar.currentCalendar()
    let CalendarOption = NSCalendarOptions()

    dateComponents.day = NumberOfDaysToAdd

    let newDate = CurrentCalendar.dateByAddingComponents(dateComponents, toDate: baseDate, options: CalendarOption)
    return newDate!
}

函数调用，将当前日期增加9天

var newDate = addDaystoGivenDate(NSDate(), NumberOfDaysToAdd: 9)
print(newDate)

函数调用，将当前日期减少80天

newDate = addDaystoGivenDate(NSDate(), NumberOfDaysToAdd: -80)
 print(newDate)

使用以下代码:

NSDate *now = [NSDate date];
int daysToAdd = 1;
NSDate *newDate1 = [now dateByAddingTimeInterval:60*60*24*daysToAdd];

As

addTimeInterval

现在已弃用。

它的工作原理!

NSCalendar *calendar = [NSCalendar currentCalendar];
NSCalendarUnit unit = NSCalendarUnitDay;
NSInteger value = 1;
NSDate *today = [NSDate date];
NSDate *tomorrow = [calendar dateByAddingUnit:unit value:value toDate:today options:NSCalendarMatchStrictly];

在Swift 4或Swift 5中，你可以使用like bellow:

let date = Date()
let yesterday = Calendar.current.date(byAdding: .day, value: -1, to: date)
let dateFormatter = DateFormatter()
dateFormatter.dateFormat = "yyyy-MM-dd"
let yesterday_date = dateFormatter.string(from: yesterday!)
print("yesterday->",yesterday_date)

输出:

Current date: 2020-03-02
yesterday date: 2020-03-01

NSDate *now = [NSDate date];
int daysToAdd = 1;
NSDate *tomorrowDate = [now dateByAddingTimeInterval:60*60*24*daysToAdd];

NSDateFormatter *dateFormatter = [[NSDateFormatter alloc] init];
[dateFormatter setDateFormat:@"EEEE, dd MMM yyyy"];
NSLog(@"%@", [dateFormatter stringFromDate:tomorrowDate]);

基于highmaintenance的回答和vikingosegundo的评论，一个工作的Swift 3+实现。这个日期扩展也有额外的选项来改变年，月和时间:

extension Date {

    /// Returns a Date with the specified amount of components added to the one it is called with
    func add(years: Int = 0, months: Int = 0, days: Int = 0, hours: Int = 0, minutes: Int = 0, seconds: Int = 0) -> Date? {
        let components = DateComponents(year: years, month: months, day: days, hour: hours, minute: minutes, second: seconds)
        return Calendar.current.date(byAdding: components, to: self)
    }

    /// Returns a Date with the specified amount of components subtracted from the one it is called with
    func subtract(years: Int = 0, months: Int = 0, days: Int = 0, hours: Int = 0, minutes: Int = 0, seconds: Int = 0) -> Date? {
        return add(years: -years, months: -months, days: -days, hours: -hours, minutes: -minutes, seconds: -seconds)
    }

}

如果按照OP的要求只增加一天，则用法如下:

let today = Date() // date is then today for this example
let tomorrow = today.add(days: 1)