Depends entirely on the type of battery. Lead/Acid (car) batteries really shouldn't be fully discharged, and even then must be promptly re-charged. The manufacturers publish typical lifetimes, which depend on the number, and depth of each charge/discharge cycle. This is further broken down by the make up of the cells. "Deep Cycle", "Starting" and hybrid "Marine/Dual Purpose" will all have different capabilities.
On the other hand, NiCad (typically "Torch" batteries, as used in small portable electronic appliances),
should be fully discharged from time to time, as they suffer from a "memory" effect. NiMh are supposedly immune from this.
Lithium types (as used in computers and phones) will be permanently damaged by full discharge, and the equipment will normally shut down before this happens.
Is it bad to "top up" the battery when its 1/2 full??????????
That's what causes the memory effect in NiCads.