What's a carrier oil? It's a non-essential oil that can be used to dilute, extend, or preserve a more volatile, precious, or potentially irritating essential oil. Carrier oils are used to dilute essential oils for massages, to make certain oils usable on children, or to keep overly strong oils from irritating the skin. Several of them are scentless, and they are sometimes used by the unscrupulous to dilute and cheapen essential oils. However, having some to use yourself is a good thing!
Jojoba oil The only oil I've used so far is jojoba, which is actually a liquid wax extracted from the jojoba bean. I selected it because it does not go rancid or need to be refrigerated, is apparently not allergenic, and because I read somewhere that its oil was similar to the structure of sebum (the oil in our skin), and so it made a good moisturizer. Using jojoba in a blend with other oils that tend to go rancid will extend their life, which is why you'll often see it sold in 10:1 dilutions with the most precious essential oils (like rose, helichrysum, and melissa). Because of all these qualities, it is probably the most commonly used carrier oil. Rosehip seed oil is a pricier carrier oil that comes from South America and apparently has some amazing skin-regenerative qualities. It's uniquely good for wrinkle reduction, spot reduction, and healing of other kinds of skin damage. It's red in color, needs to be kept refrigerated, and will begin to go bad after about a year. Its healing effects will be evident even if you dilute it to 10% in a solution, with 90% other (cheaper!) carrier oils. Anandaapothecary has a well-written article if you want to learn more. Hazelnut oil is actually a bit astringent and therefore good for oily skins who still want to use essential oil blends. It is well-tolerated by other skin types as well, though, and keeps the skin from feeling oily after application of oil blends that contain it. It tones and tightens the skin, aids capillaries, and encourages cell regeneration. I'm finding different opinions on how long it will keep, but it sounds like the refrigerator will extend its shelf life. As you probably know, seeking out cold-pressed and organic oils will assure you the most natural and untainted product.