The Crossfire E LCD mounting bracket looks pretty sturdy. Others are not so strong. On my bikes, I usually chuck the crappy plastic bracket and make an aluminium plate that's a lot stronger, which fits over the stem. You can fold the edge down so that it's held in place at the back by the top handlebar clamp screws and the front by the stem screw. The LCDs are normally held to the plastic bracket by screws, so you make equivalent holes in the plate to fix it. Anybody that touches it will realise that it's not going to come off easily.
I often park my bike in town centres and shopping malls when I go shopping. I've never had a problem in the 5 years that I've been using LCDs. I can't say whether anybody ever tried or thought about nicking one.