When you look at the medical literature, there is some evidence of benefit. For example, lavender has been shown to help with anxiety. Many essential oils show antibacterial effectiveness in laboratory studies. Several studies show that essential oils help people relax.
Be sure to read about the oils you decide to try out, and watch for allergic reaction. Some oils should not be used on direct skin, and some (citrus oils in particular) increase your skin’s sensitivity to sunlight.