Failed paint can be unsightly, that is the initial reaction upon seeing peeling paint. If that painted surface is on the inside, unless it is old lead-based paint and someone is eating it, the problem usually remains cosmetic in nature. However, if the surface with the deteriorating paint is outside, and weather-exposed, look for negative consequences.
When the failed exterior paint is over wood, expect the wood to swell and, eventually, become soft and rot. If the paint is protecting a steel surface, often the case at outside light fixtures and handrails, rust-corrosion will degrade the metal and make it weak or lead to rusty holes.
How quickly rot will develop in the wood window trim (photo above) is dependent on a number of variables. For example, is there an overhang such as a porch roof above the area that would provide some degree of shelter, is the peeling paint on the high weather-exposure south or west sides of the house? If it is well-sheltered then maybe it won't rot.
Many people look upon failing paint as a cosmetic issue when, in fact, deteriorating paint may be the first vulnerability at the exterior of the home -- a vulnerability that can result in rotted wood, moisture intrusion and, eventually, the need for major repairs.
This is another example that illustrates how deferring ongoing maintenance can result in much bigger problems than what, initially at least, meets the eye. Needless to say, in the damp Pacific Northwest this condition presents a much bigger problem than it would at a dry locale.