In the modern world it seems like children are shielded from death as much as possible, which I think is a mistake. Grief and loss are going to be a part of every life and we don't do our children any favors by removing that factor from their childhood entirely.
I don't mean it should be shoved in their faces either, but there are very good picture books that deal with death in a non-threatening, but still serious way. And if a pet dies, you aren't helping your child by just replacing it, or telling them that it ran away or has been taken to a farm.
Grief is painful, but it's good for them to learn how to deal with that pain in small doses when they are children. Help them through it, rather than trying to remove it altogether.