How can I set the maximum amount of characters in a UITextField on the iPhone SDK when I load up a UIView?
To make it work with cut & paste of strings of any length, I would suggest changing the function to something like:
#define MAX_LENGTH 20
- (BOOL)textField:(UITextField *)textField shouldChangeCharactersInRange:(NSRange)range replacementString:(NSString *)string
    {
        NSInteger insertDelta = string.length - range.length;
        if (textField.text.length + insertDelta > MAX_LENGTH)
        {
           return NO; // the new string would be longer than MAX_LENGTH
        }
        else {
            return YES;
        }
    }
There is generic solution for setting max length in Swift. By IBInspectable you can add new Attribute in Xcode Attribute Inspector.
import UIKit
private var maxLengths = [UITextField: Int]()
extension UITextField {
    @IBInspectable var maxLength: Int {
        get {
            guard let length = maxLengths[self]
            else {
                return Int.max
            }
            return length
        }
        set {
            maxLengths[self] = newValue
            addTarget(
                self,
                action: Selector("limitLength:"),
                forControlEvents: UIControlEvents.EditingChanged
            )
        }
    }
    func limitLength(textField: UITextField) {
        guard let prospectiveText = textField.text
            where prospectiveText.characters.count > maxLength else {
                return
        }
        let selection = selectedTextRange
        text = prospectiveText.substringWithRange(
            Range<String.Index>(prospectiveText.startIndex ..< prospectiveText.startIndex.advancedBy(maxLength))
        )
        selectedTextRange = selection
    }
}
I give a supplementary answer based on @Frouo. I think his answer is the most beautiful way. Becuase it's a common control we can reuse.
private var kAssociationKeyMaxLength: Int = 0
extension UITextField {
    @IBInspectable var maxLength: Int {
        get {
            if let length = objc_getAssociatedObject(self, &kAssociationKeyMaxLength) as? Int {
                return length
            } else {
                return Int.max
            }
        }
        set {
            objc_setAssociatedObject(self, &kAssociationKeyMaxLength, newValue, .OBJC_ASSOCIATION_RETAIN)
            self.addTarget(self, action: #selector(checkMaxLength), for: .editingChanged)
        }
    }
    func checkMaxLength(textField: UITextField) {
        guard !self.isInputMethod(), let prospectiveText = self.text,
            prospectiveText.count > maxLength
            else {
                return
        }
        let selection = selectedTextRange
        let maxCharIndex = prospectiveText.index(prospectiveText.startIndex, offsetBy: maxLength)
        text = prospectiveText.substring(to: maxCharIndex)
        selectedTextRange = selection
    }
    //The method is used to cancel the check when use Chinese Pinyin input method.
    //Becuase the alphabet also appears in the textfield when inputting, we should cancel the check.
    func isInputMethod() -> Bool {
        if let positionRange = self.markedTextRange {
            if let _ = self.position(from: positionRange.start, offset: 0) {
                return true
            }
        }
        return false
    }
}
Other answers do not handle the case where user can paste a long string from clipboard. If I paste a long string it should just be truncated but shown. Use this in your delegate:
static const NSUInteger maxNoOfCharacters = 5;
-(IBAction)textdidChange:(UITextField * )textField
{
NSString * text = textField.text;
if(text.length > maxNoOfCharacters)
{
    text = [text substringWithRange:NSMakeRange(0, maxNoOfCharacters)];
    textField.text = text;
}
// use 'text'
}
Use this code here RESTRICTED_LENGTH is length you want to restrict for textfield.
   - (BOOL)textField:(UITextField *)textField     shouldChangeCharactersInRange:(NSRange)range replacementString:(NSString *)string
{
    if (textField == nameTF) {
    int limit = RESTRICTED_LENGTH - 1;
    return !([textField.text length]>limit && [string length] > range.length);
    }
   else
   {
    return YES;
   }
return NO;
}
Use below extension to set the maximum character length of a UITextField and UITextView.
Swift 4.0
    private var kAssociationKeyMaxLength: Int = 0
    private var kAssociationKeyMaxLengthTextView: Int = 0
    extension UITextField {
        @IBInspectable var maxLength: Int {
            get {
                if let length = objc_getAssociatedObject(self, &kAssociationKeyMaxLength) as? Int {
                    return length
                } else {
                    return Int.max
                }
            }
            set {
                objc_setAssociatedObject(self, &kAssociationKeyMaxLength, newValue, .OBJC_ASSOCIATION_RETAIN)
                addTarget(self, action: #selector(checkMaxLength), for: .editingChanged)
            }
        }
        @objc func checkMaxLength(textField: UITextField) {
            guard let prospectiveText = self.text,
                prospectiveText.count > maxLength
                else {
                    return
            }
            let selection = selectedTextRange
            let indexEndOfText = prospectiveText.index(prospectiveText.startIndex, offsetBy: maxLength)
            let substring = prospectiveText[..<indexEndOfText]
            text = String(substring)
            selectedTextRange = selection
        }
    }
extension UITextView:UITextViewDelegate {
        @IBInspectable var maxLength: Int {
            get {
                if let length = objc_getAssociatedObject(self, &kAssociationKeyMaxLengthTextView) as? Int {
                    return length
                } else {
                    return Int.max
                }
            }
            set {
                self.delegate = self
                objc_setAssociatedObject(self, &kAssociationKeyMaxLengthTextView, newValue, .OBJC_ASSOCIATION_RETAIN)
            }
        }
        public func textViewDidChange(_ textView: UITextView) {
            checkMaxLength(textField: self)
        }
        @objc func checkMaxLength(textField: UITextView) {
            guard let prospectiveText = self.text,
                prospectiveText.count > maxLength
                else {
                    return
            }
            let selection = selectedTextRange
            let indexEndOfText = prospectiveText.index(prospectiveText.startIndex, offsetBy: maxLength)
            let substring = prospectiveText[..<indexEndOfText]
            text = String(substring)
            selectedTextRange = selection
        }
    }
You can set limit below.