The most common sump pump problem is electrical power outage causing sudden, unavoidable failure of a sump pump. Having a back up generator for the pump that is manually operated is always a good idea. However, if the primary pump fails, a generator cannot help you.
Make sure the sizing of the sump pump is correct for the volume of water. If the pump is too large, it can overwork itself; likewise, a pump which is too small will often not be able to adequately pump the water out.
Sump pumps require a need to be submerged in at least some water to cool the pump from overheating. Often, if the reservoir for the pump goes dry, the pump will continue to work and burn itself out.
The float for the pump controls the on/off switch and if the pump shifts position within the basin the float will not rise adequately for the pump to work correctly.
The basin the sump pump sits in should not be made of dirt or gravel as the debris can enter the pump and cause serious mechanical issues to the float or the on/off switch. Follow the manufacturer's guidelines specifically and directly in order to maintain proper working order and minimize any water damage.