Sprays are really easy to make:
For every 1 ounce (2 Tablespoons) of spray:
1 teaspoon of vodka or witch hazel extract
3 to 12 drops of essential oils (about 3 drops makes a 0.5% concentration, and about 12 drops makes a 2% concentration)
5 teaspoons of distilled or spring water
Add the essential oils first, then the alcohol, then the spring/distilled water. Shake gently before each use.
Shelf life is a couple weeks. For a longer shelf life (for up to a few months), omit the water, and use 6 teaspoons of vodka. Note: for some uses (like skin uses) you might not want to use that much vodka, and might want to follow the original recipe, or just reduce the water and increase the vodka a little.
For general air fresheners, I recommend using a lower concentration, unless the area you are spraying in is really stinky! The reason I recommend 0.5% concentration or less is that some essential oils are solvents or can discolor fabrics etc. Mainly these are the citrus oils (I never understood why some companies put citrus essential oils into their laundry detergent formulas, since they are mild solvents and can affect the dyes). Vanilla (Vanilla planifolia) absolute, oleoresin, or CO2 extract is heavenly. My sister loves grapefruit (Citrus paradisi) and lime (Citrus aurantifolia) essential oils!
Body and hair sprays: you can use up to a 2% concentration unless your skin is very sensitive. Good essential oil suggestions are lavender (Lavendula officinalis aka L. vera aka L. angustifolia), rose (Rosa damascena, R. rugosa, R. centifolia, R. alba), ylang ylang (Cananga odorata, available in different fractionations), or your favorite! Be mindful that some essential oils, like angelica root (Angelica archangelica) and some (and not all) of the citrus essential oils are mildly phototoxic (make your skin more sensitive to the sun). You can read about phototoxicity in this post and also in this post. If you choose to use the phototoxic essential oils, just spray your hair and clothes.
For clothes: Atlas cedarwood (Cedrus atlantica) and lavender would be good choices for clothes. They used to scent clothes in the Middle Ages with both of these herbs to keep them fresh smelling and also to repel insects. Use a low concentration of essential oils. Don't use angelica root, since it can attract insects.
To kill bacteria: 2% is fine, but if you must, you can go up to 5% (30 drops of essential oils per ounce) but mind where you are spraying (fabrics or materials)! In aromatherapy, less is best; and a 2% concentration is strong enough to kill bacteria. Most essential oils are antibacterial, but some are antiseptic, and some even are anti-viral. Lavender and tea-tree (Melaleuca alternifolia) are wonderful since they are all of these.
For body deodorant, use a 2% concentration, and also use more alcohol. Use up to 50% vodka/witch hazel to distilled/spring water. Lavender, clary sage (Salvia sclarea), the citrus essential oils, and tea tree are good choices.
General odors (trash can etc): see general air spray uses.
Insect repellent: a 2% concentration is good. Spray on your clothes, hair, and skin, careful not to get in the eyes. Good insect repellents are lavender (though flower scents can attract bees), lemongrass (Cymbopogon citratus), atlas cedarwood, patchouli (Pogostemon cablin), and lemon eucalyptus (Eucalyptus citriodora).
To apply on insect bites: lavender, blue aka german chamomile (Matricaria chamomilla) or roman chamomile (Arthemis nobilis) , and tea tree essential oils. 2% concentration.
Relax: Many essential oils are great for relaxing! Try lavender, rose geranium (Pelargonium graveolens), any of the citrus oils, rose, jasmine (Jasminum grandiflorum, J. sambac, and J. auriculatum), or whatever you like! Up to 2%.
For facial sprays, I would use a 1/2% concentration. There are many great essential oils you can use for the facial skin like lavender, rose, neroli (Citrus aurantium), jasmine, ylang ylang, and more!
Note: it's better if your spray bottle is made of glass (some essential oils eventually eat through plastic). Colored glass is best (essential oils degrade in sunlight). But if you decide to use a plastic spray bottle, just check it from time to time for leaks.
If making sprays for children, use 1/2% concentration, and research well before use. Many essential oils are not suitable for babies and young kids.
Edited March 5, 2014: minor revisions and to add a little more information. Added links to some of my other essential oil posts.