^{Note: This is an updated answer. Comments below refer to an old version which messed around with keycodes.}

JavaScript

Try it yourself on JSFiddle.

You can filter the input values of a text <input> with the following setInputFilter function (supports Copy+Paste, Drag+Drop, keyboard shortcuts, context menu operations, non-typeable keys, the caret position, different keyboard layouts, and all browsers since IE 9):

// Restricts input for the given textbox to the given inputFilter function.
function setInputFilter(textbox, inputFilter) {
  ["input", "keydown", "keyup", "mousedown", "mouseup", "select", "contextmenu", "drop"].forEach(function(event) {
    textbox.addEventListener(event, function() {
      if (inputFilter(this.value)) {
        this.oldValue = this.value;
        this.oldSelectionStart = this.selectionStart;
        this.oldSelectionEnd = this.selectionEnd;
      } else if (this.hasOwnProperty("oldValue")) {
        this.value = this.oldValue;
        this.setSelectionRange(this.oldSelectionStart, this.oldSelectionEnd);
      } else {
        this.value = "";
      }
    });
  });
}

You can now use the setInputFilter function to install an input filter:

setInputFilter(document.getElementById("myTextBox"), function(value) {
  return /^\d*\.?\d*$/.test(value); // Allow digits and '.' only, using a RegExp
});

See the JSFiddle demo for more input filter examples. Also note that you still must do server side validation!

TypeScript

Here is a TypeScript version of this.

function setInputFilter(textbox: Element, inputFilter: (value: string) => boolean): void {
    ["input", "keydown", "keyup", "mousedown", "mouseup", "select", "contextmenu", "drop"].forEach(function(event) {
        textbox.addEventListener(event, function(this: (HTMLInputElement | HTMLTextAreaElement) & {oldValue: string; oldSelectionStart: number | null, oldSelectionEnd: number | null}) {
            if (inputFilter(this.value)) {
                this.oldValue = this.value;
                this.oldSelectionStart = this.selectionStart;
                this.oldSelectionEnd = this.selectionEnd;
            } else if (Object.prototype.hasOwnProperty.call(this, 'oldValue')) {
                this.value = this.oldValue;
                if (this.oldSelectionStart !== null &&
                    this.oldSelectionEnd !== null) {
                    this.setSelectionRange(this.oldSelectionStart, this.oldSelectionEnd);
                }
            } else {
                this.value = "";
            }
        });
    });
}

jQuery

There is also a jQuery version of this. See this answer.

HTML 5

HTML 5 has a native solution with <input type="number"> (see the specification), but note that browser support varies:

• Most browsers will only validate the input when submitting the form, and not when typing.
• Most mobile browsers don't support the step, min and max attributes.
• Chrome (version 71.0.3578.98) still allows the user to enter the characters e and E into the field. Also see this question.
• Firefox (version 64.0) and Edge (EdgeHTML version 17.17134) still allow the user to enter any text into the field.

Try it yourself on w3schools.com.

1. You will only need a ScrollView if the contents you have now do not fit in the iPhone screen. (If you are adding the ScrollView as the superview of the components just to make the TextField scroll up when keyboard comes up, then it's not needed.)

2. The standard way to prevent the TextFields from being covered by the keyboard is to move the view up/down whenever the keyboard is shown.

Here is some sample code:

#define kOFFSET_FOR_KEYBOARD 80.0

-(void)keyboardWillShow {
    // Animate the current view out of the way
    if (self.view.frame.origin.y >= 0)
    {
        [self setViewMovedUp:YES];
    }
    else if (self.view.frame.origin.y < 0)
    {
        [self setViewMovedUp:NO];
    }
}

-(void)keyboardWillHide {
    if (self.view.frame.origin.y >= 0)
    {
        [self setViewMovedUp:YES];
    }
    else if (self.view.frame.origin.y < 0)
    {
        [self setViewMovedUp:NO];
    }
}

-(void)textFieldDidBeginEditing:(UITextField *)sender
{
    if ([sender isEqual:mailTf])
    {
        //move the main view, so that the keyboard does not hide it.
        if  (self.view.frame.origin.y >= 0)
        {
            [self setViewMovedUp:YES];
        }
    }
}

//method to move the view up/down whenever the keyboard is shown/dismissed
-(void)setViewMovedUp:(BOOL)movedUp
{
    [UIView beginAnimations:nil context:NULL];
    [UIView setAnimationDuration:0.3]; // if you want to slide up the view

    CGRect rect = self.view.frame;
    if (movedUp)
    {
        // 1. move the view's origin up so that the text field that will be hidden come above the keyboard 
        // 2. increase the size of the view so that the area behind the keyboard is covered up.
        rect.origin.y -= kOFFSET_FOR_KEYBOARD;
        rect.size.height += kOFFSET_FOR_KEYBOARD;
    }
    else
    {
        // revert back to the normal state.
        rect.origin.y += kOFFSET_FOR_KEYBOARD;
        rect.size.height -= kOFFSET_FOR_KEYBOARD;
    }
    self.view.frame = rect;

    [UIView commitAnimations];
}


- (void)viewWillAppear:(BOOL)animated
{
    [super viewWillAppear:animated];
    // register for keyboard notifications
    [[NSNotificationCenter defaultCenter] addObserver:self
                                         selector:@selector(keyboardWillShow)
                                             name:UIKeyboardWillShowNotification
                                           object:nil];

    [[NSNotificationCenter defaultCenter] addObserver:self
                                         selector:@selector(keyboardWillHide)
                                             name:UIKeyboardWillHideNotification
                                           object:nil];
}

- (void)viewWillDisappear:(BOOL)animated
{
    [super viewWillDisappear:animated];
    // unregister for keyboard notifications while not visible.
    [[NSNotificationCenter defaultCenter] removeObserver:self
                                             name:UIKeyboardWillShowNotification
                                           object:nil];

    [[NSNotificationCenter defaultCenter] removeObserver:self
                                             name:UIKeyboardWillHideNotification
                                           object:nil];
}