I know what you're thinking: slather oil on my face? Are you nuts?
Not so fast. There's a good explanation for the existence of oil-based cleansers, I promise. Quick chemistry refresher: like attracts like, which means the oil in an oil-based cleanser bonds with and dissolves the oil and grime on your face. This means they can work for all skin types, even oily skin, since they remove oil without over-drying the way detergent-based cleansers can.
Oil-based cleansers are also useful for removing makeup, since most makeup contains oil. The best way to know which method of cleansing gets your face the most sparkling clean is to take one of these for a test drive. There is a slight risk of pore-clogging side effects, but that is usually from the non-oil ingredients, or from not rinsing them off fully. For a few shopping ideas,
DHC's version ($11–$24) has a cult following, as does Shu Uemura's version. (That one wasn't for me, though — I broke out.) I had great luck with Laura Mercier Cleansing Oil Light ($40). Even though it is pricey, you only need a dime-sized drop to get the job done, and it removes makeup so thoroughly that there is no need for an additional makeup remover. For a few more shopping options, browse this widget.