Latin might be considered a "dead" language in regular society, but if you're deep into the traditions of the Catholic Church, or you like the Extraordinary Form of the Mass, or the Novus Ordo Mass in Latin, then knowing even the basics of the language can certainly come in handy.
As you know, a foreign language education is important. Even if you aren't into any of the above, a background in this language can be very helpful when it comes time for your student to take their college ACT or SAT tests. Knowing the language can help your students do better in vocabulary and even spelling. Many of our English words find their root in Latin.
If you still aren't convinced, give it a try and see how much fun learning even the basics can be. We've only studied the basics, but I can tell you that it has been helpful when we've attended Mass and we hear the Mass parts said or sung in Latin.
Like other languages, its good to start introducing the basics when the kids are young and then, as they get older, you can introduce them to some of the more difficult concepts. By high school, they could even be writing papers using their accumulated knowledge.
Something new to check out in the Latin department is the Little Latin Readers. They have a beginner and intermediate level. We received copies of the beginner books and I found them very easy to use. Here's how they describe their products:
"Little Latin Readers is a carefully progressing series for learning the language of the Church. The series allows Latin to come easily and naturally for students of all ages. Featuring short stories, simple poems and dialogues, these small format readers, workbooks and pronunciation CDs will give beginning Latin students an important sense of achievement and success, and insure their progress for years to come. Readers include selections about ancient Rome, Britain and Gaul, Catholic Europe, the life of Christ, Our Lady and the apostles, as well as a study of the Mass."
Like every other subject, there are many other programs to choose from. Here are a few that I've heard about repeatedly that you might want to also look into (although we've never tried any of them).