My harbor breeze ceiling fan has white, black, and blue wires coming from the motor assembly. My ceiling has 2 black and 1 white wire. The ceiling fan which I am installing has a light kit. Can I twist the two black wires in the ceiling together and connect them to the black and blue wires twisted together on the motor assembly?

Yes, you can do that.
The blue wire on your fan is the light.
The black wire is the fan.
You can connect to wire from switch(Blue and Black together).
Or if you have 2 wires coming from 2 switches, then you could have 2 separate switches.
If it happens to be in a single gang opening, you can get combo fan/light control in one device.
Or if it is single gang mudring in 4" box or extension ring, you can take 2 gang mudring,
Overlay over single gang mudring, trace out, remove just enough to remove single gang , and install 2 gang mudring, If you are careful, Wall plate will cover and no patch or paint needed. This will allow full size controls or Automation Switch.

Depends, how were the two black wires in the ceiling previously connected? If they were previously hooked together, then yes, Strat is correct.

Ceiling fan wiring - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-wiring.php)

I have a Hampton Bay fan and Harbor Breeze light kit. The fan is already installed. I just bought the light kit and I found the blue and white light kit wires in a plastic bag in the fan. However, they are not connected to anything in the fan. What must I do to connect them to the fan after I have connected them to the light kit?

I already responded to your question in your other thread.

I have the harbor breeze ceiling fan with light the wire from ceiling are black, red and white I connected white to white and black to black and blue to red wire from the ceiling it seems the red wire has power, can I connect and twist together the blue and black wire together.

What happened when you connected it the way you described?