Paint is made by combining chemicals such as solvents, binders, additives and pigments. Latex paint is water based, which means the main ingredient is water. The other main category of paint is oil-based, which means the main ingredient is some kind of organic solvent. Of the two, oil-based paint is sturdier and normally used outside or in high-humidity areas like bathrooms and kitchens. It is also usually more toxic when inhaled.
Since the base solvent in oil-based paint is white spirit, toluene, xylene or some other petroleum derivative, it should come as no surprise that breathing in fumes from this kind of paint is not entirely safe. Symptoms to watch for include headache, nausea, dizziness or extreme fatigue. These effects may be more pronounced if you are painting in a poorly ventilated area or you've been exposed to the fumes for too long even if there is good air flow. The best way to alleviate these symptoms is to get away from the painting area and find some fresh air to clear your respiratory system out.
If you continue to expose yourself to these fumes over the course of weeks, months or even years, damage can begin to manifest itself in internal organs. Long-term inhalation can lead to kidney, liver and blood problems. Purposefully sniffing paint fumes, especially from a spray can, can cause irreversible brain damage and even death on the first incident.
As you might expect, the damaging effects of oil-based paint inhalation by children can occur even more quickly than in adults. Small kids should be kept away from the painting area and open cans of paint. For the protection of everyone, put a box fan in an open window in the room being painted, pointing out, so that toxic fumes will be drawn outside. Keep the fan going like this for an additional 48 hours after the painting is done, and try to use the room as little as possible during that time. The faster the paint dries, the sooner the health danger passes.