I've heard this can be a big problem! We don't have our tree up yet (holiday fail!) so I'm not sure what's going to happen with our 2.5 year old. Hopefully she'll be ok about leaving the ornaments on the tree but she does like to collect things to take on walks around the house so we'll see. I've heard of people putting baby gates around their trees, and of course everything fragile goes up, up, up!
I've heard the baby gate thing too! I usually just resign that the kids will grab the lower ornaments, so we put a ton of stuffed animal, non breakable ones down there- it looks a little goofy, but then I don't stress about it.