Many Buddhist traditions practice Metta Bhavana, or loving kindness meditation. (Metta means loving-kindness.)
The way I do it is as follows.
The meditation is in several stages (the classic version has five). At each stage I silently recite a mantra, linked to the breath. The first line is said on the inbreath, the second on the outbreath, and so on.
May you be happy
May you be well
May you be safe
and free from injury
May you be filled
with loving kindness.
This is a shortened version of the full mantra, and therefore easier to remember.
The first stage of the meditation is to wish yourself loving kindness (so the mantra is "May I be be happy, may I be well..." etc).
The second stage is to wish loving kindness to someone you love.
The third stage is to wish it for someone you like.
The third stage is to wish it to someone you are neutral towards.
The fourth stage is to wish it to someone you dislike, or who has hurt you. (Don't start this one by trying the most difficult person in your life, as it can be quite painful - start small and work upwards.)
The fifth stage is to wish loving kindness to a small group such as your immediate circle of friends (or you can imagine the previous four people together in a group).
The sixth stage is to wish loving kindness to your immediate community (place of work, spiritual community or neighbourhood). At this stage I send loving kindness to Wiccans and Unitarians everywhere.
The seventh stage is to wish loving kindness to everyone on the planet.
The eighth stage is to wish it to all sentient beings.
The benefits of this meditation are manifold. It is very calming and soothing; it allows you to focus on your breath, and relax into feelings of loving kindness and safety; it helps you to feel connected to all beings, and to expand your imaginative sympathy to encompass them; and it helps you to overcome negative feelings towards people you dislike, which can really improve your relationship with them, and help you to forgive them. It also has beneficial effects on the brain, as it has been shown to reduce the "fight or flight" instinct in situations where it is not needed.