Personally, I avoid chemical mosquito repellents. Most contain Deet, which is toxic and potentially fatal if swallowed, so why would you put it on your skin where it will be absorbed into your bloodstream? High does or long term exposure of Deet have been associated with neurological damage, and it can damage some plastics and synthetic fabrics, cause rashes, swelling, and eye irritation at the very least.
For a natural mosquito repellent, I've found citronella is effective, but it doesn't last very long. Citronella oil is extracted from cymbopogon nardus and cymbopogon winterianus grasses, is considered harmless to people, but the smell repels insects. Catnip oil has also shown promise in a recent study. I haven't test this yet, but rosemary or sage thrown on barbecue coals is supposed to be effective as well. Most other natural means of repelling mosquitoes that I've read about didn't appear to be that effective.
It turns out that neem oil and coconut oil combined make a great natural mosquito repellent too. If you're following a natural, chemical-free lifestyle, you probably already have a bottle of Neem Oil, or have read about it's useful properties for killing fleas and ticks on your pet, mites and fungus in the garden, etc. Another good anti-fungal and anti-bacterial is coconut oil. It is very helpful for dry skin and eczema, both as a topical cream and food additive. I combined 1 part neem oil with 4 parts coconut oil, and rubbed it on my skin, and it worked very well against mosquitoes.
The neem and coconut oil mix has been tested in a field study in the village of District Mandla, where mosquitoes are quite fierce. Results showed up to 91% protection for 12 hours against mosquitoes.
Neem oil is a natural vegetable oil from the neem tree in India. Leaves and seeds contain sallanin, an effective repellent of mosquitoes, and is safe to use around children and animals. If you can't find it and the coconut oil locally, they are both available online.
