I agree with Will. That sort of thing happens to spider plants which are either over watered, underwatered, over fertilized or if there's a build up of minerals in the soil from your water source. In such a case it would need to be flushed with filtered or rain water.
... At first I thought bacterial blight. Since the brown tips would indicate such a thing. But now I'm not so sure. I don't see any yellowing on the sides of the leaves. You might want to remove the damaged leaves though, to be on the safe side.