On touching the negative terminal of battery, shouldn't this negative charge flow to earth? On batteries one terminal is clearly mentioned as negative.  I wonder can we neutralize this terminal by just touching it with finger?
In electrostatics it is common to neutralize a charged object by touching it and thus letting excess charge flow to ground. 
 A: Technically, you can neutralize the electrostatic potential of the entire battery this way.  However, batteries do not primarily work by electrostatics.  They work by creating a potential difference between the two terminals which encourages electrons to flow out of one (the negative side) and into the other (the positive side).  This encouragement is provided via chemical reactions.
If you were to touch the negative terminal, you would move enough electrons into or out of the battery to ensure that the negative terminal is "neutral" with respect to the ground.  At this point, there is still the chemical reactions going on which ensure the positive terminal is at a small poitive voltage (i.e. 12V for a car battery).  this potential will not go away simply because you "grounded" the negative terminal because there's no electrons flowing in a loop from negative to positive outside of the battery, and positive to negative within the battery.
There are some corner cases where a reasonably large number of electrons might flow out of the battery into the ground.  However, that number pales in comparason to the number of electrons that the battery is ready to cycle through an electrical connection between positive and negative terminals.  
Using my favorite metaphor for electricity, a garden hose, grounding one terminal of a battery is like pouring all of the water out that's sitting stagnant in the hose.  Yes, water does come out, but that static amount of water is nothing compared to the amount of water that flows dynamically through that hose when it is turned on.
If you are a numbers person, we can explore what happens to the battery in terms of voltages.  Remember, voltages are always measured between two things.  There is no such thing as absolute voltages.  However, we can assign something, such as the ground, an absolute voltage of 0V, for simplicity.  We could assign this 0V value to anything, but assigning it to the Earth is very common.
Let's say our battery is on a plastic shelf.  The negative terminal might be at -500V (that is to say 500V lower than the potential of the ground).  This may seem high, but it isn't.  Electrostatics typically involve higher voltages than other electrical circuits.  Voltages of 1000V+ are common, and the voltages can be in either direction depending on how the charge got there!  I choose a negative voltage simply because you talked about electrons flowing into the ground.  The only way we'll get that behavior is if the battery is negatively charged.
Because there is a chemical reaction in the battery that is trying to keep a 12V difference between the positive and negative terminals, the positive terminal will be at -488V (-500 + 12 = -488)
Now, you take your shoes off, and touch the negative terminal.  You are a decent conductor, and the negative terminal is at -500V while the ground at your feet is at 0V, so current is going to flow.  The excess electrons in the battery will flow into the ground, potentially generating a spark.  As it does so, the voltage on the terminal will shift to 0.
While this is happening, the chemicals inside the battery are still trying to keep a 12V differential between positive and negative.  However, half way through the discharge process, the negative terminal would be at -250V.  That's 238V different from the voltage of the positive terminal, far greater than the 12V the chemicals are inducing.  As a result, electrons begin flowing from the positive terminal to the negative terminal (which seems backwards, but we have to remember that we've been busily raising the voltage of the negative terminal by pumping electrons into the ground).  Thus the voltage on the positive terminal also moves in the direction of 0.
Eventually all of the excess electrons have been moved off into the ground.  The negative terminal is actually at 0V, just like the Earth.  Now, because of the chemicals in the battery, we still find the positive terminal is 12V higher than the negative terminal, at 12V.
In the end, we moved the negative terminal from -500V to 0V, and the positive terminal from -488V to 12V.  There's still a 12V difference between them.  Some electrons moved out of the battery, into the ground.  How many moved into the ground is dependent on something called the capacitance of the battery.  However, what matters is that the battery is still ready to deliver power to a car, even though it has been "neutralized" in an electrostatic esense.
A: No.  The battery is already neutral, and remains neutral during operation. (-ve charge leaving one terminal has to be replaced at the other terminal.) If some -ve charge flowed to Earth the battery would become +ve, attracting electrons back to it.
A: 
I wonder can we neutralize this terminal by just touching it with finger?
  In electrostatics it is common to neutralize a charged object by touching it and thus letting excess charge flow to ground. 

In short yes, if initially the finger has higher electric potential than the battery negative terminal and no current is flowing through the battery, then the battery behaves as bodies in electrostatics.
But, even then, that kind of neutralization removes only some of negative charge from a conductive body, not all of it. When potential of the body reaches potential of the ground, the process stops and there still may be some charge left on the body. We just don't notice it since its electric field is too weak.
Charge on a negative battery terminal is usually quite small to begin with and easily influenced by approaching/touching with other charged bodies. In theory, the negative terminal's net charge could have zero or even positive value - just connect that terminal to a large positively charged body.
A terminal of a battery is called negative not because it itself has net negative charge, but because it has lower potential than the other terminal in the usual setting where it either is disconnected or it supplies energy. If a battery supplies energy to simple element such as bulb via wires, the negative terminal will be releasing electrons to the wire, and positive terminal will accept electrons from the wire. In such dynamic situation, it may be difficult to permanently remove charge from its terminal, because it can be partly resupplied from the circuit.
