I apologize in advance for the length of this post, but you clicked it - you must be interested!
There have been many, many topics posted here that are basically the same questions - can I use this fan? Will this fan work? Which fan should I use? What's the best fan? Hopefully I can get all the information together here in one place and finally "blow the lid off" this whole fan thing.
Please note - I am not talking about sealed rooms with CO2 enrichment. These setups will require very specific fans and air routing, to ensure the benefit of the additional c02 is recognized.
First off - Lets dumb it way down - there are basically 3 uses for fans in a growroom.
1. Air Exchange - This is the process by which fresh air is introduced to and removed from the grow room, in order to provide the plants with fresh CO2. Most air exchange setups will have to be coordinated with #3 - cooling and odor control to ensure optimum results for stealth.
2. Air circulation - This is internal air movement in the cabinet/room - plants waving in the breeze. It is required to help strengthen stems and promote air movement to make sure the C02 is actively moving around, able to be taken up by the plants.
3. Cooling and/or odor control - These are the fans used to power a carbon scrubber (to exhaust warm stinky air from the room) and to blow across the lights to lower temperatures in the grow room.
Static Pressure - the fans natural predator
This definition from Wikipedia defines Fluid Static Pressure, but the applicable excerpt for pneumatic duct pressure is highlighted
"In fluid mechanics, and in particular in fluid statics, static pressure  is the pressure exerted by a fluid at rest.
Examples of situations where static pressure is involved are:
The air pressure inside a latex balloon is the static pressure and so is the atmospheric pressure (neglecting the effect of wind).
The hydrostatic pressure at the bottom of a dam is by definition the static pressure and so is the pressure exerted on one's thumb when stopping the water flow in a garden hose.
The pressure inside a ventilation duct is not the static pressure, unless the air inside the duct is still.
On an aircraft, the pressure measured on a generic point of the surface of the wing (or fuselage) is not, in general, the static pressure, unless the aircraft is not moving with respect to the air."
^ Thx to Wikipedia
In other words, the higher static pressure the intake air ambient state is, the harder it is for a fan to pull the air, the less the output of the fan will be. Fan CFM numbers quoted by manufacturers are almost always advertised for the flow at 0" static pressure, since this will always be the highest number. The better manufacturers will give you ratings at various static pressures. Ducting, bends, filters, and reductions/objects(i.e.lights) in the intake (or exhaust) create a harder path for the fan to suck and blow through (suck through a McDonalds straw and then through a coffee stirring straw). Put a box fan 1/2 inch away from a wall, blowing towards you. When it is next to the wall, the fan needs to pull air through the small gap all the way around the fan casing, thereby limiting the amount it can blow out. Now, move it farther from the wall (making this gap larger). The fan finds it easier to pull air through this larger gap and will blow harder. Now put it in a window or the middle of the room, and the fan will be working as it was intended. This same principle of "restriction" is demonstrated by large duct runs, ribbed ducts, bends, carbon filters, and is the single reason two fans that move the same CFM can become vastly different outputs when dealing with a small amount of restriction.
Types of Fans
"There are three main types of fans used for moving air - axial, centrifugal (also called radial) and cross flow (also called tangential).
The axial-flow fans have blades that force air to move parallel to the shaft about which the blades rotate. Axial fans blow air across the axis of the fan, linearly, hence their name. This is the most commonly used type of fan, and is used in a wide variety of applications, ranging from small cooling fans for electronics to the giant fans used in wind tunnels.
The centrifugal fan has a moving component (called an impeller) that consists of a central shaft about which a set of blades form a spiral pattern. Centrifugal fans blow air at right angles to the intake of the fan, and spin (centrifugally) the air outwards to the outlet. An impeller rotates, causing air to enter the fan near the shaft and move perpendicularly from the shaft to the opening in the scroll-shaped fan casing. A centrifugal fan produces more pressure for a given air volume, and is used where this is desirable such as in leaf blowers, air mattress inflators, and various industrial purposes. They are typically noisier than comparable axial fans.
The cross flow fan has a squirrel cage rotor (a rotor with a hollow center and axial fan blades along the periphery). Tangential fans take in air along the periphery of the rotor, and expel it through the outlet in a similar fashion to the centrifugal fan. Cross flow fans give off an even airflow along the entire width of the fan, and are very quiet in operation. They are comparatively bulky, and the air pressure is low. Cross flow fans are often used in air conditioners, automobile ventilation systems, and for cooling in medium-sized equipment such as photocopiers"
^ Thx to Wikipedia
For our purposes, we will only be interested in the first 2 types of fans -
Centrifugal Blower Fan - Commonly referred to as a Squirrel Cage fan, also technically known as a shaded pole blower, the exhaust is offset from the intake and requires a flange to mount to ducting - Dayton and Active Air are examples of these. Blowers are modestly priced and can be excellent for any of the three purposes we need them for.
Centrifugal Inline Fan - This is a Centrifugal Fan which has identical inlets and outlets on each side, and as such is ideal for use in ductwork. Fantech, Vortex, and Panasonic Whisperline are examples of manufacturers. These can also be used for any of the three purposes, although generally higher priced (and MUCH quieter) than a comparable CFM squirrel cage fan..
Axial Fan - PC Fans, Muffin Fans, Gable fans, Attic Fans, Box fans, Duct "Booster" Fans, Oscillating fans - Any fan that blows air directly across the axis of the fan is considered an axial Fan. Highly affected by static pressure, for the most part, axial fans are only efficient for #2 - air circulation
While a cross-flow fan could be utilized, output, size and price are not attractive for this purpose.
How much fan do I need?
In one word - more.
Personal Opinion Warning!
Note - this section is from opinion and experience cobbled together with rudimentary pneumatic/HVAC management knowledge and common sense learned over my 38 years. I have constructed ~20 or so different grow rooms/areas, from 150W cabinets to 5KW rooms and each one had its own problems and solutions. The only one size fits all solution is to buy the biggest baddest fan made - hardly an option
This question is extremely hard to answer without accurate duct static pressure readings, configuration, room dimensions and plans, intake/ambient temps, desired results/temps,light wattage,acceptable noise level, number of plants, reflector design, stealth issues ... All these differences add up to make each growspace and setup unique in their requirements. 2000 watts in a 10x10x10 room in Alaska is a lot different than 600 watts in a C-13 in Brazil! The smaller cabinet will likely have more heat problems, and use a single fan for more than one purpose, hence a single powerful fan. The 10x10x10 room you might get away with 2 box fans, one circulating air and one pointing out a window (not very stealthy though) The only safe answer to the question "what size fan do I need" is "a larger one".
In cabinets, for air circulation and exchange, I like to shoot for an air exchange of at least 3x per minute. I also always put a small fan inside the cab simply for circulation - no intake/exhausts, just to move air, blow across the tops of the plants. Computer fans can work great for this. Say you have a cabinet that is 2' x 2' x 6' - this equals 24 cubic feet (LxWxH = Cu Ft. - If using inches for measurement, then divide the answer by 1728 (24x24x72= 41472 cubic inches. 41472/1728 = 24 cu ft) The minimum size fan I would use for this box would be ~ 75cfm. That does not take into account any ducting, cooling, or routing requirements - just air exchange and circulation. If I was using a scrubber (and not concerned about anything else), personally I'd double it to a 150cfm fan, either squirrel cage or centrifugal, depending on budget and other needs. This is my starting point.
After you have your starting point, put the lights on in the cabinet WITHOUT the plants, and take accurate temperature readings inside, once the lights have been on for a few hours. Note that if you leave the thermometer in the direct light, it will read much higher than the ambient/actual temperature. Shade the thermometer probe and locate it about mid cabinet to get a more accurate temperature reading. Check the temps of the room the cabinet is in, taking care to note situations such as a box inside a closet with the door closed - with no place to exhaust the air outside of the closet - the temperature of the whole closet will gradually raise, raising the intake temps more, which makes hotter exhaust, and continues this cycle.
If your cabinet temp is less than 80 degrees, congratulations - you are done. Get a fan the size of your starting point and go go go!
The rest of us will have a, in some cases, huge temperature differential (74 degrees intake air, 110+ degrees in the cabinet in the shade for example). Lights and ballasts put out a lot of heat. So not only does the fan need to circulate and exchange air, it needs to remove 30ish degrees as well. Heres where it gets tricky, and is very important to know where the exhaust is going, what the intake temperature is, how the fixture can be cooled. Most reflectors have fittings on either end of them, making it very easy to hook up to ducting. My rule of thumb is an additional 75 cfm for each 10 degrees differential. So if using a scrubber in this 2x2x6 cabinet (150cfm starting point + 150cfm for light cooling) I would size ~ 300cfm for cooling, odor control and air exchange. Then we would determine noise requirements, budget and mounting options, and decide between a squirrel cage or centrifugal fan in the desired CFM range.
Though it may seem overkill, using this formula I have rarely ever had to resize a fan - and never cooked a plant to my knowledge. This formula accounts for static pressure from typical corrugated duct routings, usually 6-inch in diameter, and a couple of 90 degree elbows, and a passive intake (or 2) of 2x the exhaust size exit. Slight adjustments should be made for convoluted duct runs, 4-inch tubing, and any other special requirements. Temps are almost always in control from day one, making less hassles in the long run. Don't cheap out and buy the least expensive fan you can find, make sure its from a reputed manufacturer with a warranty and you will be much happier.
Complete rooms are a different task altogether, although the same methods are used for determining ambient temps. Since the air is not contained in a cabinet, I wouldn't be as strict on the 3x a minute exchange rate, nor will there be the same intense heat concentrated in a small area. A larger room will almost always be easier to keep cool and fan sizing is generally determined by circulation and odor control requirements
I can't get a new fan - what can I do?
Some people cannot afford a new fan, or have no room, or are trying to use an inadequate fan and refuse to upsize - whatever the reason. Theres only a couple of solutions here - keep cabinet doors open, increase intake size (if inadequate), lower the intake temperatures, or remotely locate the ballasts outside the cabinet. other than that, theres not much else you can do to remove heat from the growspace.