I sincerely hope you won't give in and simply allow your children to watch anything they want to watch–or that their friends watch. Images they see now will be with them the rest of their lives, shaping their minds and molding their characters–for good or for ill.
After all, as a loving parent, you do everything you can to protect your children from physical harm. Why shouldn't you do the same to protect them from emotional, moral and spiritual harm? Simply allowing your television to become a glorified baby-sitter isn't wise–but when it spills out a steady diet of violence and sex, it cannot help but harm your children and distort their values.
I know this is not a simple issue; you need to be wise in setting the right limits, so your children don't become resentful or unprepared for life's challenges. Don't be negative, but let them know why you're concerned about this. In addition, plan special times of family fun, so they grow up with happy memories of their childhood.
Most of all, pray for your children, and ask God to help you point them to Christ. And remember the Bible's admonition, both for them and for you: "Do not conform any longer to the pattern of this world, but be transformed by the renewing of your mind" (Romans 12:2).