The picture of my DM screen in the first post also shows a transparent, plastic cube.
As a dungeon master, I like my players to feel a little sense of jeopardy, a small sense that their character might not survive this combat. Rolling my dice in the open enhances that drama at the table. The players know I’m not fudging rolls to spare them–or to pick on their character.
I like when a tense moment brings players to their feet, and when everyone at the table watches to see the outcome of a roll. In one memorable moment, I reminded a player that his movement would provoke a pair of attacks, but he cockily laughed off the risk. I rolled a pair of natural 20s and the table burst out laughing. If I had rolled behind the screen, and simply announced a pair of crits, the event would fallen as flat as a card trick on radio.
Despite all this, I would rather not kill any characters (unless this is Lair Assault, when I will coup de grace your dying body). One of the virtues of fourth edition is that the system prevents a couple of bad rolls from turning into a dead character.
Rolling in front of a DM screen raises the problem of keeping the dice corralled. I roll into a transparent, plastic box purchased from a craft store. Unlike a big tray, the box packs easily, takes little space on the table, and never hides the outcome of a roll.
Update: I use this Containables 3-1/2″ x 3-1/2″ x 5″ Plastic Container with Removable Lid. It comes in a set of 4, but I can no longer find just one of anything similar.