Okay, so my DS (9yo) and DD (7yo) actually are in the minority of NOT losing/forgetting things. But DS made up for it this spring when he forgot his rented VIOLA at school over SPRING BREAK. Arghhhh, replacement cost is ~$800!! I was worrying for ten days, but thankfully the viola was still in the HALLWAY outside of his classroom when school resumed. So, never left anything behind before...but when he did, it was a BIG BIG item!
IMHO, labeling stuff that goes to elementary school only helps you identify which item is yours if there are multiple items just like it in the lost & found. I walk past the lost and found and it seems like most "big" items (eg. coats) HAVE names in them but there isn't someone "in charge" of the lost and found, looking at each item that comes in and tracking down the child, the classroom, etc to return it. It is the child's responsibility to go look for the item. (Camp can be a different story).
At their AfterCare program, they can bring stuff from home in 1 Friday per month. I always make sure the kids know that if that item is lost, it will NOT be replaced so that is a chance they need to decide to take. DS's friend brought his DSi (handheld video game) and another child borrowed it and then "returned" it to another child's backpack by mistake. It took several days before the DSi surfaced, but it eventually did. While it was still missing, DS said to me "it is a good thing Santa brought Kevin that DSi, otherwise his parents would be really upset about losing all that money" LOL!!