If you have sensitive skin or allergies, consider getting tested so that you know what your exact sensitivities are—that way you'll know what you truly need to avoid. If you're already aware of your reactivity to fragrance, there are several gentle options to keep you hydrated. If you need something super mild and basic, try Nature's Baby Organics Face & Body Moisturizer. It's exactly what it sounds like, and it's predominantly a blend of aloe, olive oil, coconut oil, and calendula. In a similar vein (but slightly more adult), there's Kiss My Face Olive & Aloe Moisturizer, which has a grand total of six ingredients and absolutely no scent.
Alternately, if you want fragrance free that's still heavy on other bells and whistles, Elta MD AM Therapy Facial Moisturizer is a lightweight, unscented formula that also manages to contain everything from caffeine and willow bark to allantoin.