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When I search on Amazon for eg. neutral density 67mm, I get long list of different filters. Some of them are marked like: ND2, ND4, ND8 etc. I'm guessing this means 2-, 4- or 8-stops filter, am I right?
But what about filters, that say 0.6 or 0.9? What does this mean?
Is there any other thing (apart of stops and diameter) that I should also pay attention to when choosing a filter?
The number associated with an ND filter is actually the denominator (bottom) of a fraction.
So an ND2 filter should be thought of as 1/2 the amount of light being allowed through the filter. For example, setting the lens at f/2.8, and using an ND2 filter would make that an f/4 situation for a total of 1 stop difference.
ND4 filter is allowing 1/4 the light (which is half of ND2) thus a 2 stop difference.
Continuing, ND8 is 1/8 and three stops and, although I've never seen them, an ND16 is half as much light as ND8 so would be four stops less light.
The decimal numbers you mention (0.6, 0.9) are another system of quantifying the density of the ND filter. These numbers are the log (base 10) of the factor by which the light is reduced. (This is sometimes called the absorbance). So for example a 1 stop filter reduces the amount of light by a factor of 2, and log(2) = 0.3 so a 1 stop ND filter is ND0.3 in this system. Similarly 2 stops is 0.6 and 3 stops is 0.9. The combined effect of multiple filters is obtained by adding up the numbers. For example a 1 stop, 2 stop and 3 stop filter combined (6 stops in total) would be 0.3 + 0.6 + 0.9 = log(2^6) = log(64) = log(2) + log(4) + log(8) = ND1.8.
I would highly suggest the best quality GLASS filters you can afford. Cheaper (especially plastic) filters will tend to add nasty color effects. Although technically color casts can be corrected in post, cheap filters also can also reduce the quality of light meaning things like more chromatic aberation.
Lastly, don't worry about getting the highest ND number, I carry two filters around and stack them together, when needed, for combined affect. Which is more reason why quality filters matter as stacking simply magnifies imperfections too!
For the ND's that use decimals (i.e. .3 .6 .9), each .3 is one stop less light that reaches the sensor. So, a .9 means a 3 stop deduction in light to the sensor.
For the ND's that use a number (i.e. 8X), they operate under the power of 2 exponentially. So, an ND 16 is a 4 stop deduction in light (2 to the 4th power is 16).
There are two common ways of quoting ND filter strengths, and one less common:
2x, 4x, 8x, etc. Sometimes these are referred to as ND2, ND4, ND8, and so on. These refer to the amount by which the light is diminished. An ND2 filter halves the light, while an ND8 filter reduces it to one eighth.
1 stop, 2 stops, 3 stops etc. Sometimes these are referred to as EV, for exposure value. These are probably the most convenient measurement because they tell you how many stops they'll adjust your exposure by.
Numbers like 0.3, 0.6, 0.9 etc. These are basically just 0.3 x the number of stops of EV. These are less common.
Each stop of exposure value refers to a halving of light, so:
1 stop = ND2
2 stops = ND4
3 stops = ND8
4 stops = ND16
And so on.
Stacking multiple ND filters adds stops, and multiplies strength values.
So, ND500 sounds like a lot, but it'd be the same as stacking an ND16 and an ND32 (16 x 32 = 512; manufacturers round it to 500).
There are three different widely accepted systems used to describe the transmissive properties of filters.
One of the systems you have used in your question is called the ND x.x number system and is used by Lee and Tiffen to describe their filters. It is the only system that uses decimals in the notation. The decimal values are based on optical density, not f-stop reduction. An ND 0.3 filter has a one-stop reduction in terms of f-stop, as half the light striking the filter is allowed to pass through. An ND 0.6 has a two-stop reduction as 1/4 of the light passes through. An ND 0.9 rating is a three-stop filter. Each increase of ND 0.3 results in one additional stop of light reduction. So an ND 1.8 is a six-stop filter, while an ND 2.0 is 6 2/3-stop filter, and so on. Note that 0.3 is approximately the Log(base 10) of 2.
The other system referenced in your question, used by Hoya, B+W, and Cokin, is the ND 1/x (or 1/2^x) system. Each filter is described as the reciprocal of the amount of light allowed to pass through the filter. An ND2 allows one-half the light to pass for a one-stop reduction. An ND4 allows one-fourth the light to pass for a two-stop reduction, an ND8 allows 1/8 the light to pass for a 3-stop reduction. An ND64 filter allows 1/64 the light to pass for a six-stop reduction. Note that each increase of one stop in this system is a power of the number "2".
Another system, used by others is the ND1xx notation. All of the numbers begin with a "1" and include two other digits. The second and third digits express the number of stops of light the filter reduces. An ND 101 filter is a one-stop filter, an ND 102 is a two-stop filter, and ND 106 is a six-stop filter, and so on.
To see a chart that shows each system and how filters in one system relate to filters using one of the other notations, please see this chart at wikipedia. This chart also shows the optical density (0.3, 0.6, etc.), f-stop reduction (1-stop, 2-stop, etc.), % transmittance (50%, 25%, etc.), and fractional transmittance (0.5, 0.25, etc), for each step in each system.
1st Specification: Divide log(ND number)/log(2) to get the number of stops. Examples:
2nd Specification: Divide the ND number by log(2) or 0.3 to get the number of stops. Example:
