There are reasons for and against doing this.
Firstly, leaving your water feature on all the time can be expensive as most pumps run on electricity.  Secondly, there is a risk of the pump burning out from being in constant use, or if there is a sudden loss of water (sometimes this can be caused by e.g. storms where the water gets blown over the side of the pool surrounds or fountain).
Keeping the pump running 24 hours a day does however prevent the pump becoming calcified and this can in turn mean that it lasts longer.  However, we recommend that anyone planning to do this keeps a close eye on their fountain to mitigate the risks mentioned.