Indeed, there are many different types of "wall warts" - the question here was specifically about a plug-in USB power supply for a cell phone, so the voltage regulation will be excellent.
AC-DC Power Supplies - Using Wall Warts is an article I wrote a few years ago that discusses the different types of power supplies available and provides test data for a number of 12 volt switchers.
For wall warts, there are 4 major types:
Transformer - AC - AC supply. These will be cube shaped and relatively heavy for their size. The AC output requires rectification, filtering and regulation. There are very limited times this would be an optimal choice.
Linear AC DC supply. These use a line frequency transformer, so they will be cube shaped and heavy for their size. These supplies usually have only rectification and minimal filtering and do not include voltage regulation. Under no load conditions, the voltage will be (much) higher than the nameplate voltage. This type of supply is really only useful supplying a voltage regulator. This type of supply is being used less and less, in favor of more efficient switching supplys.
Switching AC - DC Constant Voltage Supplies: these are the cell phone, laptop and in general the low voltage DC supplies used to power most electronic products now-a-days. They are generally not a cube shape and are relatively light for the power provided. The output voltage will be close the the nameplate voltage across the rated load range. In my experience, most of these handle overloads by reducing output voltage and handle shorted outputs gracefully.
Switching AC - DC
Constant Current Supplies: These are becoming more common and are used to power LED lights. They have the physical characteristics of switchers above but provide a constant current at a varying voltage. If the rating is something like 315mA, 0 - 8 volts, it's a constant current supply and only useful in limited cases, light powering LED lights.