Performing partner yoga poses builds a high level of trust and intimacy. It can be a fun exercise to do with children, or a special moment shared between lovers.
Benefits of Partner Yoga Poses

Working through a yoga sequence with someone else extends a number of benefits:

It's non-competitive fitness in which two or more people can engage.
It builds intimacy, especially between love partners.
A deeper level of trust develops between two yogis who explore the spiritual nuances of the craft together.
Partners can assist one another with more challenging asanas or help with guided meditation.
It's a fun activity to share with children.
Shared touch therapy in the form of yoga is similar to a massage. The spirit is revitalized with the gentle touch, the even flow of breath, and the focused attention on one another.

General Guidelines of Partnering

When you team up with another yogi, keep in mind that everyone has a different level of skill and flexibility. There may also be some underlying conditions, such as back injuries, problems with carpal tunnel, and other maladies that prohibit individuals from performing the same postures.

Take the time to review some basic asanas with one another, such as the foundational ones found in Hatha yoga. After practicing poses familiar to the both of you, move on to poses that are more challenging to do with someone by your side.

Always respect the body's limitations, and never force a pose. Remember, the overall goal of performing yoga together is the improved mental, physical, and emotional wellbeing of everyone involved.

Popular poses two or more can do include, but are not limited to:

Child's Pose: Perform facing one another, and maintain eye contact.
Tree Yoga Pose: Extend arms out toward one another for better balance.
Warrior Pose: Any of the three versions help both of you build strength.
Downward Facing Dog Pose: "Spot" your partner to make sure the pose doesn't strain the back.
Triangle Pose: Face one another and perform in unison, or help check your partner's form.
Side Plank Pose and Plank Pose: Build strength together, or help your partner keep a straight and level back.
Camel Pose: For a real challenge, ease into this backbend and face one another upside-down!
Pigeon Pose: Draw up into this pose with the help of each other, or extend toward one another.
Frankly, any yoga pose can be converted to a dual or group pose, depending on your intent.

Find a Partner Class Near You

Look on Yoga Finder to find classes that perform partner yoga, or put out a query on Yoga Meetup to see if anyone else is interested. A group of potential partner session attendees joining together is strong persuasion for any local studio to create a class and make it worthwhile.

Many yoga instructors also conduct one-on-one sessions with instructors to perfect a pose and enhance the overall experience.

Partner Yoga DVDs and Books

If there isn't a partnering class near you, here are some helpful resources to use so that you may perfect partner yoga poses with a friend or companion:

The book Yoga for Partners: Over 75 Postures to Do Together, by Jessie Chapman, demonstrates a variety of couple postures in vivid photography. Instructions detail how to synchronize breathing and movement for an unbeatable yoga experience. The book also lies flat when open, so you and your companion can focus on the movement.
Another popular book is Partner Yoga: Making Contact for Physical, Emotional, and Spiritual Growth, by Cain Carroll and Lori Kimata. It features both individual yoga poses and yoga flow sequences. This book also features family-oriented postures so that you can get the kids involved.
Many practitioners also believe that performing partner yoga poses is the ultimate expression of having no boundaries. Aaron Star's Hot Nude Yoga: Partner is a widely-popular DVD for those who want to expand on the exploration of touch and yoga, based on the teachings of instructor Aaron Star of Hot Nude Yoga in New York. And yes, as the title of the DVD clearly states, the featured yogis, mostly male, are nude, so if you're not comfortable with that, this may not be the disc for you.
You can also try the DVD Dynamic Partner Yoga with instructor Glenda Twining. It focuses on building strength and intimacy between partners at any yoga level.