A simplified version of the accepted answer that does NOT require you to type names of properties manually in every property setter like OnPropertyChanged("some-property-name"). Instead you just call OnPropertyChanged() without parameters:
You need .NET 4.5 minimum.
  CallerMemberName is in the System.Runtime.CompilerServices namespace
public class Sample : INotifyPropertyChanged
{
    private string _propString;
    private int _propInt;
    //======================================
    // Actual implementation
    //======================================
    public event PropertyChangedEventHandler PropertyChanged;
    [NotifyPropertyChangedInvocator]
    protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
    {
        var handler = PropertyChanged;
        if (handler != null) handler(this, new PropertyChangedEventArgs(propertyName));
    }
    //======================================
    // END: actual implementation
    //======================================
    public string PropString
    {
        get { return _propString; }
        set
        {
            // do not trigger change event if values are the same
            if (Equals(value, _propString)) return;
            _propString = value;
            //===================
            // Usage in the Source
            //===================
            OnPropertyChanged();
        }
    }
    public int PropInt
    {
        get { return _propInt; }
        set
        {
            // do not allow negative numbers, but always trigger a change event
            _propInt = value < 0 ? 0 : value;
            OnPropertyChanged();
        }
    }
}
Usage stays the same:
var source = new Sample();
textbox.DataBindings.Add("Text", source, "PropString");
source.PropString = "Some new string";
Hope this helps someone.