If it's BOTH the washer and dryer then I would suspect your electrical.

I am assuming this is a gas dryer and your talking about the standard plugs that you plug in your coffee maker, etc. I am also assuming you live in the US and we are talking about the same type of plug. If this is an electrical dryer, DON'T plug anything else in this outlet. And if it is an electrical dryer, you need to call someone unless you are an electrician. It could be that your plug is not wired correctly to the back of the machine. If you don't have a clue about electrical, again call someone qualified before dealing with the dryer connection.

Otherwise, I would suggest you check your plugs with a radio or something that makes a sound when it's running and plugged in. That will tell you if it's your appliances or your electrical circuit. It could be that your appliances are on a GFCI (ground fault circuit interrupter) somewhere else in the house and it has tripped. Someone may be unknowingly pushing the re-trip button when they find the plug doesn't work in the room that they are currently using.

On the GFI's, I have some in the kitchen and in one of the bathrooms, but I also have one in the master closet and one in the garage. One GFI can control more than just one plug. And not necessarily in the same room. So expect to look for them in the not so obvious places.