nikon d7000 - Why are these black dots / spots appearing in my pictures?

I took some shots recently and I noticed that I'm getting a lot of little black dots in my images.

I cleaned my lens thoroughly with the Nikon camelhair brush and retook the pictures but once again, the dots appear.

I'm shooting with a Nikon D7000 and using a starter lens. I've attached an example (notice the black spots on the chairs, on the ceiling, etc).

Answer

Nikons have a reputation of coming from the factory with a little too much oil on the shutter mechanisms. Some of the excess oil eventually finds its way onto the sensor. What you are seeing in your photos is the shadow of the oil (and the dust stuck to it) on your sensor. You will probably have to go through several cycles of cleaning your sensor before the problem will gradually go away. Any type of dust spots on the sensor (actually on the IR filter in front of the sensor) will be darker, sharper, and more noticeable when shooting with narrower apertures than when shooting with wider apertures.

For more on why dust spots are darker and sharper using narrower apertures, see Question About the D600 Dirty Sensor Test - Why Use a High f-Stop? and Why use a small aperture when trying to see sensor dust?

As to how to clean you sensor, please see What is the best way to clean the sensor on a digital SLR?