First let's establish exactly what we are talking about.  Sometimes humans attach different meanings to the same word and they end up talking at cross purposes. To me intimacy is much broader than sex. It is a deep sense of knowing, understanding and belonging that is far more important, harder to achieve and longer lasting than having sex. It has more to do with who and what you are than sexual ability. You can have sex without intimacy, even with a marital partner. You can have an intimate relationship without sex. I think its important to know that these two concepts are not 100% linked to each other. When the two do coexist in the same relationship, that's a keeper that will regenerate your batteries forever!

Some forms of intimacy other than sex? 

1. Sharing meaningful things/activities of any kind that you can both relate to and therefore relate more deeply to each other. That might be art, music, a book, whatever shares a piece of you with that other person. Having 'your song' is very intimate. Whenever you hear it played no matter where you are, its meaning is a bond you share with each other only, even if you are surrounded by thousands of people at a concert.
2. Being kind to each other in ways that are just for the two of you. It may be a common jesture but have meaning to you because it demonstrates the respect and caring you have for each other. It could be as simple as opening a door for the other or helping them on with their coat. It could be doing a chore they usually do, such as clean off the table to show that you understand and appreciate all they do for you.
3. Giving of yourself fearlessly. You can be intimate with your partner without opening your wallet. Take a walk in your favourite park. Put on his/her favourite TV show and make popcorn. Draw him/her a bath with candles and scent and dim lights and then close the door and give them alone time.  Go to church if that has meaning to you.

Sex is great but intimacy gives your relationship the strength to last.