We discovered a great website this summer called Scriptures 4 Kids. I love it because it has 4 versions, or levels, of Book of Mormon stories for kids. There are also games, and other fun activities. I should have my kids write the review, they are on there more than I am.
Immediately following devotional we have what we call "Scripture Reading Time". The kids each get to go to a different station each day. Computers is one station and they are allowed to do things on the computer that involve the gospel, so Scriptures 4 kids has been a great addition to their scripture reading time.
Other activities that they do on the computer are, LDS.org, friend.lds.org, newera.lds.org, scriptures.lds.org, scripturescouts.com.
One thing to note about scriptures4kids, it doesn't work consistently in Firefox, so make sure you use internet explorer.