NSDate *today=[NSDate date];
NSCalendar *calendar = [[NSCalendar alloc] initWithCalendarIdentifier: NSGregorianCalendar];
NSDateComponents *components=[[NSDateComponents alloc] init];
components.day=1;
NSDate *targetDate =[calendar dateByAddingComponents:components toDate:today options: 0];

你可以使用NSDate的方法- (id)dateByAddingTimeInterval:(NSTimeInterval)秒，其中秒为60 * 60 * 24 = 86400

NSDate *now = [NSDate date];
NSCalendar *calendar = [[NSCalendar alloc] initWithCalendarIdentifier:NSGregorianCalendar];
NSDateComponents *components = [calendar components:NSYearCalendarUnit|NSMonthCalendarUnit|NSDayCalendarUnit fromDate:now];
NSDate *startDate = [calendar dateFromComponents:components];
NSLog(@"StartDate = %@", startDate);

components.day += 1;
NSDate *endDate = [calendar dateFromComponents:components];
NSLog(@"EndDate = %@", endDate);

iOS 8+， OSX 10.9+， Objective-C

NSCalendar *cal = [NSCalendar currentCalendar];    
NSDate *tomorrow = [cal dateByAddingUnit:NSCalendarUnitDay 
                                   value:1 
                                  toDate:[NSDate date] 
                                 options:0];

Swift 4更新:

let now = Date() // the current date/time
let oneDayFromNow = Calendar.current.date(byAdding: .day, value: 1, to: now) // Tomorrow with same time of day as now

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)