Used to be such devices were called "vampires." Two pointy teeth sucking up a little bit of power. Although some of them have a ground pin as well as the two ordinary pins.
Most devices with transformers have more than just transformers. They usually have rectifiers and batteries and a circuit to charge up the batttery. Some examples are the charger for your phone or other such hand-held device, the power supply for your lap top computer, the backup power for your LED alarm clock, etc. They have an isolation transformer to reduce the possibility of ground fault. Then there is a rectifier of some kind. Then a cirucuit to check out your batttery level and decide if it needs charging. Possibly one or more LEDs to indicate their current operating mode, whether they are connected to the AC power, if the battery is charging or charged, maybe some other things.
Such devices usually consume a very small amount of power when the main device is not in use. If you leave your phone charger plugged in it will be using a small amount of power all of the time. Same for your lap top charger, etc.
There was a push during they early 2000's to try to get people to switch to devices that used less standby power. The idea is that, even if they only use a few watts each, there are 10's of millions of them. Anybody with two or three hand-held devices will have similar numbers of them. Maybe more since they might have one for the office and one for home. You might find it annoying to have to carry your charger around, and they are usually not too expensive. So it might be the case that having people unplug these things when not in use would save many MW of power in a large city. It would be possible for the device to know when something was plugged in for charging and only use power when it was. However, the media chose to mock the president at the time for calling them "vampires." So this particular thing went away.