A lot of homeschoolers and mothers of preschoolers ask me which foreign language they should first teach their child (children). If your children are young (as in 6 or younger) - I would make this recommendation. If there is a language which you know well, then obviously start with that language. If your family heritage is Russian, and you are planning a trip in a year or two, learn Russian with your children. Even if you don't speak the language, you can learn with your children by watching a video together (such as Bilingual Baby in Russian) or listening to an audio CD (Teach Me Russian) or doing a software program together (Vocabulary Builder Russian).
I guarantee your child will learn faster than you, though! If there is no connection to another language, you can either start with a more difficult language, such as Chinese or Arabic - making your child quite marketable when they are older, or an easy language such as Spanish - there are plenty of materials available and native speakers with whom to practice. Just make sure you have an audio program, dvd or software, where you can hear native speakers and learn the correct pronunciation from the beginning.
It is always nice when you and your children can actually use the language without having to travel far - just choose a restaurant for dinner where you can practice what you have learned!
If you never thought of teaching a foreign language before and your child is still in elementary school - see the above. If they are in middle to high school, Latin is a good choice. In my opinion, the benefits of Latin to everyone are to strengthen their knowledge of the English language in terms of both vocabulary and grammar and to help in preparation for tests such as the SAT. I think Latin is better taught in middle and high school than to elementary school students, and would welcome a discussion on that subject. Romance languages such as French and Spanish can help with English vocabulary as well.
However, you still need to study a spoken language that is used today to communicate. Speaking properly in another language becomes harder and harder the older you become. You need materials - whether audio, video or software where you can hear pronunciation by native speakers.