An electric fireplace will cost about as much to run as an electric room heater. Many units come with multiple settings, so you would have options such as a 750 watt setting or a 1500 watt setting, letting you choose based on how much heat you need.
The actual monthly energy cost will vary depending on electricity prices in your area, but chances are you're not going to see a huge increase in your electricity bill unless you're going to leave the unit on 24/7.
Most people flick on their electric fireplace for a bit of ambiance in the evenings. It can also be more efficient to turn it on and heat up the room your family is in, as opposed to turning on the whole-house heat and warming up square footage that isn't even in use. An electric fireplace is actually quite efficient when it comes to zone heating so could save you money if used in that manner.
These days, you can purchase a basic unit for less than $200, so it's a fairly inexpensive comfort for the home when compared to other types of fireplaces.
If you're trying to decide, here are a few things to consider: