If it's still not clear, then you need to study transistor theory. I tried to cover everything in a small space, so I hope cramming in so much information was not confusing. This way, the motor will only run when it's connected to the positive terminal of the battery through another suitable resistor, typically 300 to 500 Ohms. If the transistor is not connected to a microcontroller, then you have to bias the base by connecting it to the negative side of the battery through a suitable resistor (typically 3K to 4K). I'm talking about the digital output connected to the base of the transistor through a resistor. Once you solve the problem with the motor turning on by itself, then you can turn the motor on intentionally by setting the digital output of the micro-controller HIGH. However, this only works if the micro-controller and motor are powered by the same battery and turned on and off at the same time by a physical switch. You can dispense with this if you're using a micro-controller, because this can be done by setting a digital output LOW and connecting it to the base through a suitable resistor (typically 1K). The base should be pulled down by connecting the base of the transistor to the negative side of the battery through a suitable resistor, which biases the base and prevents the motor from turning on erratically. Next, you said 'I don't give any input to base', I'm not sure exactly what you mean by that, but when you get the emitter and collector connections fixed, you can't leave the base floating or the motor will probably turn on. In this case, the diode's arrow (the banded side of the diode) should point toward the positive terminal of the battery to shunt reverse current when the transistor turns the motor off. Don't forget to use a protective diode across the motor, or you'll destroy the new transistor.

You have probably destroyed the transistor by now, so you should replace it and this time ground the emitter to the negative terminal of the battery through a suitable resistor and connect the motor between the collector and the positive terminal of the battery. This is something that often confuses students, thanks to schools and text books that emphasize 'conventional current flow' over electron current flow. In a schematic diagram, electrons from the negative terminal of the battery flow against the arrow symbol in transistors and diodes. In an NPN transistor the negative terminal of the battery goes to the emitter. I agree with AWOL, you have the connections to the transistor reversed.

Npn transistor base collector emitter