Last time I went to the US I travelled with a laptop and spent a lot of time taking it out at airport checks and removing the battery from it. This time I may be travelling with an iPad - do they make you do the same (minus battery removal) for tablet computers, etc? I.e. remove them from your luggage and scan them separately.
Since I've gotten my new iPad (3), I've been leaving it in my backpack and taking it through airport security checks without any problems. The rules explicitly refer to laptops. The original risk was that someone could remove the electronics of a laptop and replace them with explosives. With laptops getting thinner and thinner that is less likely, but they go by the old rules. I assume tablets are too thin to pose a risk. They still have an x-ray of the inside as it goes through the scanner.
This depends largely on the sort of case in which you carry your computer.
In 2008, The TSA began publishing guidelines for Checkpoint-friendly laptop bags. If you carry your computer in one of these kinds of cases, you shouldn't need to remove it. The key takeaway points are that:
If you carry your laptop in a bag that does not meet these standards, such as a backpack or messenger bag, you'll need to remove it. The electronics in a laptop are complex and detailed, and in order to get a clear view and ensure they haven't been tampered with, the TSA wants to make sure that these devices pass through the scanner relatively unobstructed.
Regardless of whether your bag is deemed 'laptop safe', if a TSA agent feels that your laptop warrants additional screening - whether because of the case, an irregular design, or for whatever other reason, they can and will ask you to remove it from it's case. Similarly, while you are not required to remove the battery from any device proactively, TSA agents may request that you do so (if possible) in order to more closely inspect it.
For the purposes of these rules, Smaller electronic devices, like tablets, e-readers, and even smaller netbooks/notebooks like the Macbook Air DO NOT need to be removed from your luggage unless explicitly requested by a TSA agent for further inspection. You should be able to leave these devices in your luggage and send it through the X-Ray machine without issue.