Why is this circuit letting the smoke out?
OK, let's start with your schematic. In order to have even a hope of working, your schematic must look like







simulate this circuit &ndash; Schematic created using CircuitLab

Let's assume your 7805 is working correctly (although you should measure it to be sure). Then the base current should be about 4 mA. For a fully-saturated transistor you can figure on a gain of about 10, so if the normal motor current is 40 mA or so you'd be in good shape. But of course, your motor is not 40 mA. Instead, you think it's 200 to 300 mA. Worse, that's probably when running. As has been commented, if the rotor is not moving, you can figure on something like at least 5 times as much - let's figure on 1 amp. Then in the circuit shown, the motor resistance can be modeled as about 12 ohms.

The first thing you should notice, on page 3 of the data sheet is that this is probably more than the absolute maximum current the transistor is rated for, so even if you drive the transistor successfully you'll likely be in trouble. But it's unlikely that this particular issue is your problem.

Let's say that, since the transistor is not saturated, it is operating at a gain of about 100. Then the collector current will be about 400 mA. The voltage drop across the motor will then be on the order of 0.4 x 12, or 5 volts. This will leave 7 volts across the transistor, and the total transistor power dissipation will be 7 x 0.4, or 2.8 watts. 

Go back to the data sheet, and you'll see that this is about 5 to 6 times the absolute maximum power for this transistor. This really should be a clue that your circuit won't work.

So. First, you must measure the DC resistance of your motor. Use a standard meter and don't let the rotor turn. This determines the current you must switch. It also gives you an idea of the size transistor you need. And never, never assume you can run a component like a transistor at absolute maximum - it's a really good way to kill components when you do something you didn't figure on. In this case, get a transistor rated for twice the expected current. Now, find a transistor which will handle the current.

Assuming you're using a BJT, figure your base current is the motor current divided by 10. Size your base resistor appropriately.

And in the future, if you want advice, don't guess what your circuit needs - measure it. 

ETA - It seems likely that you do not have a DMM (Digital MultiMeter). Get one. No arguments, no complaining, no whining. Just do it. You can get them cheap on eBay, although I'd stay away from the really cheap Chinese versions. Until you can measure voltages and currents in an operating circuit, and measure resistances in components, you are operating blind as to what is going on. 
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