There have been recent patent fights (such as Apple v. Samsung) that seem to claim certain basic physical forms of devices, such as a smartphone, can be patented. Aren't there a limited number of possible shapes possible? Does patent law allow one company to own a simple shape such as a rectangle with rounded corners for a type of machine?
The Supreme Court recently addressed the issue of whether abstract ideas, like basic shapes, are patentable. In Bilski, the court held that:
The concept of hedging, described in claim 1 and reduced to a mathematical formula in claim 4, is an unpatentable abstract idea, just like the algorithms at issue in Benson and Flook. Allowing petitioners to patent risk hedging would preempt use of this approach in all fields, and would effectively grant a monopoly over an abstract idea. -- http://www.patentlyo.com/patent/2010/06/bilski-v-kappos-business-methods-out-software-still-patentable.html
However, trade dress violations are redressed by an entirely separate and distinct body of federal law than patents.
The answer to your question is that yes, the number of shapes is limited, and no, a company cannot patent a simple shape. However, trademark and trade dress provide protections for all types of shapes. Think about all the company logos which use geometric shapes.
This is a specific type of US patent filing. It relates to the underlying form and style of the device. Apple said that a 'white rectangle' with 'large borders/margins' and 'curved corners' was their 'signature' design features for a 'flat tablet' computer device. The jury agreed (very strongly).
I personally don't agree this type of patent should be used so broadly, or provide protection that strong. That said, the Apple court argument does have some merit.
The British / Common Law approach, providing protection against "Passing Off", is (IMHO) a much better approach. This protects anyone (even without specific 'design' patent filing) from a product (particular an inferior one) from being too close in exact appearance.
I hope (in the Apple / Samsung case) the jury finding is overturned or weakened on appeal, to be closer to "Passing Off" protection, and simply requiring Samsung to diverge enough in their design.