Your sensor requires cleaning. How often depends on a lot of factors, from the environment you're shooting in and how often you swap lenses to whether you hold your camera up or down when changing lenses (hint: hold it so the sensor well faces down, so any dust in the air won't settle on it).
If you have a new body, it may come with a sensor cleaning mode (using a rapid vibration of the sensor to knock the dust off). use it: I turn my camera body off and on prior to every shoot. If I'm in a dusty situation and changing lenses, I turn it on and off occasionally during shoots. I also turn my camera off before changing lenses. First, it forces a sensor cleaning before and after every lens change. Second, some people have claimed that a sensor that's powered up can carry a static charge, and that static charge will attract dust to the sensor, so you want your sensor powered off when the chamber is open. I don't know that this is true, but my old canon 30d sure acted that way. It was a true dust collector.
If you have an older body without sensor cleaning, do it yourself. Use an air blower on a regular basis to clean the sensor. I used to do it before every shoot, and I used to do it at the end of every shoot (now my bodies have the auto-cleaning. I don't use an air blower unless that doesn't solve the problem. Id' rather leave the chamber closed and not expose it to dust)
At some point the blower won't remove the dust. Moisture can "weld" a piece of dust to the sensor so the blower won't remove it. This is more common in humid locations, and it is more likely to happen if you don't get in the habit of regular cleanings of the sensor via the vibration or blower method.
At that time, you'll need to wash your sensor using brushes and solvent. This step scares more photographers the first time or two they do it; it's not THAT bad, but you need to be careful. There are various products for this; a good site to investigate options is http://www.cleaningdigitalcameras.com/
If your camera hasn't been cleaned in a good while, I recommend a professional cleaning. Find a local camera shop and have them do it, or sites like http://www.borrowlenses.com/ will let you ship the body to them and they'll do it. This can run $35US to $70US, from what I've seen. I also think it's a good idea to let the pro clean the sensor once in a while (like once a year under typical use) whether you think it needs a wet cleaning or not.
If you're seeing dust spots on your images, clean your sensor. If you haven't cleaned it for a while, let a pro clean it, then learn how to keep it clean on your own. Buy a good air blower, pick up a wet cleaning kit for your camera. Get in the habit of dusting off the sensor before you start to remove whatever settled in while it was idle, and at the end to remove anything that showed up while you were shooting. That'll limit the chance of a fleck of dust welding itself to the sensor requiring wet cleaning. Learn to wet clean and get comfortable doing it in your home BEFORE you need to do it in an emergency and in the field. Trust me on that.
This is all something that should be part of your regular camera maintenance, along with wiping clean bodies and lens bodies and removing fingerprints from lenses and filters. If you get in the habit, you'll have fewer problems to fix in post (I hate dust specks), you won't have a badly placed dust spec ruin an unfixable image, and your gear will typically last longer. And you won't end up in the field trying to find a moderately clean area out of the wind to do an emergency clean-ectomy on the sensor because a dust spot's welded right where you want your subject image to be...