I am a newbie to photography and shoot with Canon 550D ( Rebel T2i ) that can take 3 bracketed shots at a time. I want to know whether 3 shots are typically enough to capture the different lightings in the scene. I know that a lot depends on the particular scene I am shooting, but is it possible to know a generic answer for landscapes like beaches, sunset etc? I ask this cos I get to go to scenic places infrequently and its very difficult to experiment and learn there. If 3 are not enough, I can change the exposures manually and take a few more shots.
It all depends on the scene in terms of overall brightness, the total dynamic range, and how fine the graduations are between bright and dark.
The wider the difference is between the brightest part and the darkest part of the scene, the further apart your darkest and brightest exposures need to be.
The best way to measure this is to use your camera's smallest metering circle (usually called "spot metering") and compare the recommended exposure values between metering the brightest part of the scene and metering the darkest part of the scene. How many stops difference are there?
Once you have determined how far apart your darkest and brightest exposures need to be then you can decide how many exposures you need based upon the maximum step size between exposures. If your scene is mostly very bright and very dark with no gradual transitions then you can probably get by with larger steps. Something in the range of 2 or even 3 stops between exposures will probably be enough. If the scene has a lot of gradual transitions from bright to dark then you will need the steps between exposures to be smaller. Differences in the range of 1 stop or even less will give the best results.
Since your camera's dynamic range is usually only maximized at base ISO, it also depends on the ISO setting you are using. As you raise the ISO, your camera's DR will be reduced so you will need to use smaller steps between each exposure to capture the same amount of information. For a wide dynamic range scene you can still usually get all of the mid-tones without any gaps by shooting a -2, 0, +2 or even -3, 0, +3 series if you are shooting at fairly low ISO (around ISO 400 or less) and center your base exposure value properly. At higher ISO settings you may need to shoot a -3, -1, +1, +3 series or even a full series separated by only one stop.
Be aware that a single 14-bit raw file may contain as much dynamic range information as a a -3, 0, +3 series of 8-bit JPEGs! So shooting a series of raw shots bracketed at -1, 0, +1 includes a lot of overlap, even with digital cameras that can only capture 10-11 stops of dynamic range. The best cameras today can go as high as 13-14 stops at base ISO. Those same cameras at around ISO 3200 are down to around 10 stops of dynamic range. Not only does this affect the maximum difference between the brightest and darkest details that they can record but it also reduces the smallest step size in brightness that they can differentiate. So a sky that is bright on one side of the frame and dark on the other side will show smoother transition from light to dark at lower ISO. At higher ISO you have a greater risk of getting banding in the same transition.
Three exposures are often enough, and so are two. While there are scenes that need more, you have diminished return for every additional exposure.
Consider that a single frame from a modern DSLR can capture at least 10 stops, sometimes over 14, two frames can potentially hold 20+ stops of dynamic range. You need some overlap though so that it can be merged, so if you use +5 EV stops, you will get 15-19 stops for a 2 frame bracket or 20-24 for a 3 frame one. That is quite a lot of dynamic-range and most scenes would fall within that.
Remember, even if you have clipping somewhere, your image is not ruined. We know that details in very bright areas or deep shadows are not always visible. No one expects to look at a sunny beach scene an notice sun spots.
In practice, when the scene has a large dynamic range, you need to take many exposures despite the fact that in theory a few exposures suffice to cover the entire dynamic range. You may want to limit the exposure time for a very dark part of a scene. When shooting with a tripod at night there may be some wind causing unsharpness due to shaking when you expose for too long), this means choosing a higher ISO but that reduces the dynamic range as pointed out in Michael's Clark's answer and you'll need more exposures to cover the dynamic range of the scene than you would expect based on the typically maximum 14 bit dynamic range of the camera.
But there are other effects that make it difficult to construct HDR images using just a few exposures. Less than optimally exposed areas will have more noise, ideally you want each part of the image to be not too far from being optimally exposed on some exposure. Also, it is good to have multiple pictures with the same exposure allowing you to reduce the noise and remove moving objects in each exposure. If e.g. there is a moving dark car in one long exposure, then the HDR algorithm will flag the affected area as an extremely dark area causing an artifact there. While there are some clever algorithms that will try to automatically mask this area out of this exposure, it will still have to fill in the gap using the other less optimal exposures, which means that there will be more noise in that area.
Another problem one has to deal with is the so-called blooming effect. Overexposed pixels will leak their charge to neighboring pixels, this can make some of these other pixels to overflow as well, causing the charge to spread some distance away from the actual bright area. This blooming effect will make dark areas right next to bright areas invisible if you only have a few exposures to work with.
Since what you are ultimately interested in, is the overall quality of the image, other factors apart from the dynamic range will also be in play and these may add to the number of pictures you'll have to take. I've already mentioned noise, another factor is the field of view. While you can zoom out with a zoom lens, this will reduce the resolution. Stitching images to create a panorama will yield a superior picture.
So, you may arrive at a scene thinking that 3 pictures will do, but you may find that to cover the field of view you need to take 4 pictures and it's better to take each picture in 5 different exposures and to reduce the noise you may want to take 5 pictures for each exposure. So, you see that minor issues have increased the number of pictures you need to take from 3 to 100 even though for each issue we just need a few pictures (a few for the field of view, a few for the dynamic range, and a few to reduce the noise).
Getting enough practice with taking a large number pictures using a tripod and remote control is thus quite important. You also need to practice with aligning the pictures and processing them using software you feel comfortable working with. The best way to practice this is at home where you have full control of a scene and where you can practice as often as is necessary.