Is there a way to enable word wrapping of text on some simple widgets like QPushButton?

Use a QToolButton instead of a QPushButton. QToolButton can use multiline text and QToolButton's size is easier to control than the size of a QPushButton.

I have solved the problem with wordwrap on a button this way:

QPushButton *createQPushButtonWithWordWrap(QWidget *parent, const QString &text)
{
   auto btn = new QPushButton(parent);
   auto label = new QLabel(text,btn);
   label->setWordWrap(true);

   auto layout = new QHBoxLayout(btn);
   layout->addWidget(label,0,Qt::AlignCenter);

   return btn;
}

For word wrapping in regular QPushButton you can implement proxy style class derived from QProxyStyle.

/**
proxy style for text wrapping in pushbutton
*/
class QtPushButtonStyleProxy : public QProxyStyle
{
public:
    /**
    Default constructor.
    */
    QtPushButtonStyleProxy()
        : QProxyStyle()
    {
    }

    virtual void drawItemText(QPainter *painter, const QRect &rect,
        int flags, const QPalette &pal, bool enabled,
        const QString &text, QPalette::ColorRole textRole) const
    {
        flags |= Qt::TextWordWrap;    
        QProxyStyle::drawItemText(painter, rect, flags, pal, enabled, text, textRole);
    }

private:
    Q_DISABLE_COPY(QtPushButtonStyleProxy)
};

And later in your own MyQtPushButton:

MyQtPushButton::MyQtPushButton()
   : QPushButton()
{
   setStyle(new QtPushButtonStyleProxy());
}

See additional information on QProxyStyle class in Qt documentation.