You will get varying values on each read. A pin’s input is said to be floating if nothing is connected, which in simple terms can be explained as it just acting as an antenna for whatever electric noise is present in your environment. Its state is unknown, and utterly meaningless. If you hold a spinning electric motor close to the pin, you can see the values rise and fall more clearly.
Use a high value (10K or more) pull-down or pull-up resistor to partially mitigate this jitter. A pull-down would bring the read value down to around 0, and a pull-up would bring it up to around 1023.
Furthermore, it’s a good idea to always smoothen out analogRead (5-10 reads, ~25-50ms apart, average the values out) to get a good reading if precision is important. This is especially valid if you use longer wires, have an unshielded case, or use a switched mode power supply. Twisting the wires (GND and wiper IIRC, otherwise correct me) to a potentiometer helps.
Edit: You can use
pinMode( A0, INPUT_PULLUP ); - it provides a 20-50Kohm pull-up, though I don’t trust this and always use 1/4W resistors instead. It saves space though, and is quite handy.