Yes you can. There are a couples things to think about when it comes to breathing.
If you hyperventilate you will blow off too much CO2, causing a respiratory alkalosis. Changes in pH outside normal homeostasis have many effects, none of which are good. This is linked mainly to respiratory rate.
There is also the total volume of each breath, tidal volume. If the volume inhaled is too high, the pressures in the lung go up. High pressures in the lung can cause trauma to the lung parenchyma leading to many lung pathologies. This is usually only an issue on patients on a mechanical ventilator.
Together, tidal volume and respiratory rate make up the minute ventilation, a volume of breaths over a minute. High minute ventilation can be caused by a number of things, and is an important clue in clinical medicine.