I've had good luck with Picaridin based repellents, still a chemical, but works as well as (or better than) DEET, does not reek like DEET, and does not melt plastic like DEET, doesn't irritate skin like DEET. You can get Natrapel wipes and sprays at most outdoor/camping stores. The most common truly natural alternatives usually include mixes of Citronella (lemongrass), Geranium, Lavender, Peppermint, and/or Eucalyptus oils. The biggest difference between repellents is not so much effectiveness, but how often you need to re-apply the repellents. Even if you are taking an anti-malarial, you still want a repellent, malaria is not the only parasite mosquitoes carry and there's enough other bloodsuckers out there that can pass on some nasty things.
As a side note, Campsuds makes a bio-degradable camping soap with Citronella, Lavender, and Peppermint oils that keeps the bugs off of you while you shower (and leaves you smelling minty-fresh). Otherwise, Dr. Bronner's Lavender is a classic standby.
This is (most likely) overkill, but as a backup measure, I often get a Permethrin (another chemical, generally "safe" around people and dogs, BUT toxic to cats) based clothing treatment. Sawyer seems the easiest to get hold of.
I've had the best luck with Malarone, one of the more expensive anti-malarials, but doesn't have the nasty side effects of the 'quines and doesn't wreck your gut flora like (the MUCH cheaper) Doxycycline (broad spectrum anti-biotic [leaves me exhausted with the full run of symptoms you would expect from a harsh antibiotic regimen]). Note that with any anti-malarial, you really don't want to be taking them for the long term (usually one to two months at the most).