I have two appliances: one is old dryer which does not have a neutral, only 3 wires, black, red, and green; another one is a new oven which have 4 wire 30amp 240v. I want to know it is very important to have the neutral. I know it is in 120v. Can anyone help me with it? Thanks!!

Some 240 Volt Appliances use 120 volt items as well, and should draw current through the Neutral, NOT the Ground .
Ground is NOT to carry current except during a fault.
New Construction and remodel require 4 wires. If just changing an appliance, it is not required.

Using the 2008 NEC as a reference point.

Between the years 1942 and 1996 you were allowed ground the frames of appliances via the Neutral (Grounded) conductor.

After 1996, you were required to use a four wire circuit and the frames could only be grounded to the equipment grounding conductor.

So, if your home was built prior to 1996, you are allowed (Grandfathered) to continue the practice of grounding the frames of appliances to the Neutral.

However, if the appliance you are using requires a four wire feed, then you must run an entire new circuit from the panel to the appliance outlet.

Older appliances might not have needed a neutral. Case in point, a simple water heater. A water requires only 240 volts.

If however, the appliance requires the use of 120 volts , say for control panel circuits, then neutral would be required.

So after 1996, a green grounding wire must be used for grounding the frames of the appliances. But what is the neutral is for if the four wire feed is needed for a 240v?

This is getting confusing. WHERE is this green wire you speak of?

A typical US electric dryer, even an older one, is a 120/240v appliance. NOT a "240v" appliance. These definitely require a neutral. If this is the case with yours the cord/lead you have is wrong and has been from day one.

Really, I talked to someone from an appliance store here. He said I needed four and 240v. But I am not very sure what in general a neutral is for in a 240v where there are three service entrance condutors, two hot wires and one white wire . I know a neutral is a return in a 120v. But how about in 240v? Thanks

Okay, back to basic electricity.

Electricity that comes into your home from the power company is a "single phase" source.

If you were to draw a vertical line and split it in the middle you would have two poles (top to bottom) that are 240 volts apart.

The line splitting the middle would be exactly 120 volts apart from both of the poles.

So if you were to measure from the middle line to the top, you would have 120 volts(AC).

The same would be true if you were to measure between the middle line and the bottom pole.

The line in the middle is called the "Neutral" because it is midway between both poles.
It also serves another purpose. It is called the "Grounded" conductor.

Think of it this way, with three pieces of rope lay them horizontally from left to right. Now the top rope is 120votes as is the bottom rope.

Electricity works on a circuit. Power goes out on one line, gets used by the "Load" and the unused portion returns to the source via the Neutral.

If you need only 240 volts, there is no need for a neutral, because you do not need to create a zero reference point.

However, if the equipment (dryer) needs both 120 volts and 240 volts then the neutral is required. Whit the neutral you have voltage that is 120 between the top and the neutral point.

Clear as mud?

New Construction and remodel require 4 wires. If just changing an appliance, it is not required. Code(unless of a change I am not aware of, they constantly change)
At your Service Entrance, the neutral and ground are connected to the same point, You now have 4 conductors from your service, not 3, From that point on you have 4 conductors, 2 hots a neutral and a ground. The neutral caries current, the ground does NOT.
If you try to measure voltage between the ground and neutral, it will be Zero as both are connected at the Service.

Here is a wiring diagram to illustrate Don's explanation.

However, the Neutral is not called Neutral because it is in the middle.

It is technically the grounded conductor, and it is Neutral because it is at zero volts potential, which occurs simply because it is grounded.

The practice of allowing an appliance to use one wire for both neutral and ground was stopped because the neutral is current carrying when 120 volts is being used.

The equipment ground is a safety to drain any current that may energize the metal frame or housing of an appliance due to a short circuit.

Most if not all residential dryers need both 240 volts for the heater elements, and 120 volts for the motor and control.

The issue is not if the neutral is needed or not, it is needed. The issue is on new 120/240 volt circuits to a range or a dryer, now must use a separate equipment ground from the frame of the appliance back to the panel.

An older existing dryer circuit with only 3 wires, and the neutral and equipment ground is connected at the dryer and shared, is allowed to remain.

If at all possible, it would be wise to replace any 3 wire cable with a 4 wire cable, but NOT required by Code, for an existing cable.