Don't take me wrong, there are indeed lots of specific reasons to scan at 300 dpi, or even 600 dpi:
I've been suggesting that 300 ppi is excessive image size for video screens, but don't take me wrong, there are indeed many specific reasons to scan at 300 ppi, or even 600 ppi, even if the screen is not likely one of them.
300 ppi color or grayscale images are both expected and sufficient for commercial prepress purposes, assuming glossy magazines at 150 lpi, scaled to final size on paper (Chapter 6). The absolute highest quality art books or annual reports might benefit from 400 ppi. Newspapers are happy with 150 to 200 ppi images, at final size.
Photo quality inkjet printers want 250 to 300 ppi images (scaled to final size), but anything over 300 ppi is a real stretch of the imagination. Improved detail at up to 300 ppi is sometimes detectable on the sharpest images, and I often aim for 300 ppi. It's a very subtle difference, and even when not imaginary, it is lost altogether if viewed at arms length. 240 ppi is typically fine, and 150 ppi is enough for plain paper, or very large images, and sometimes for less sharp snapshot images too.
Printing line art mode is a common reason for using 300 ppi. Fax is 200 ppi line art and it's usually insufficient quality. We need 300 dpi, and printing line art images at 600 ppi can be optimum. For line art, it is indeed appropriate to scan to match the dpi resolution of your printer (I said line art, I intentionally excluded Color and Grayscale). If your commercial output device has 1200 dpi or 2400 dpi capability, then even interpolated resolution can be helpful for line art to reduce the jaggies (however there is normally no real benefit beyond 800 or 1200 ppi). In my opinion, interpolated resolution is only useful for line art (see Chapters 10 and 13).
300 ppi line art for OCR of course, almost always. Perhaps 400 ppi is better for the smallest text, but excessive ppi can be detrimental to OCR accuracy. More about OCR in Chapter 10.
Enlarging a scanned image to print twice as large on the printer will require doubling the normal resolution. Printing three times size needs 3X resolution, for example, scan at 600 ppi, scale to print at 200 ppi for 3X size. There are some serious IFs and BUTs concerning this, and there is more about it in the next chapters.
When scanning a small postage stamp sized area for the purpose of enlarging it. This also applies to scanning small film. 35 mm film needs to be scanned at 2700 ppi to print 8x12 inches at 300 ppi (9x enlargement). Scanning any one inch square of a photo print at 300 ppi will produce a 300x300 pixel image. Scanning it at 600 ppi gives 600x600 pixels. 600x600 is still not a large image and the larger size may be needed. This certainly does not imply that a photo print necessarily contained that much actual detail, probably it didn't, but the size is there, and sometimes we want size for the sake of size.
Scanning at high resolution, typically 2X the actual requirement, is a standard tool to eliminate moiré interference patterns when scanning images from printed material (books, magazines, newspapers, postcards, more in Chapter 12). There are other methods too, like the Descreen filter in the scanner's software.
A graphic artist doing extensive pixel level editing may want to keep all the parts very large until complete (better buy more memory).
Perhaps for archival purposes of important images, when all the future uses for the image may not be known now (better buy more disk).
You want to brag to your buddy, "Hey man, my image was 100 megabytes, and the swap file hasn't stopped yet!" <grin>
And of course, there are very many cases when 300 dpi would be inappropriate too. It depends on the requirements of the job. Instead of the above list, most of us will typically be scanning color photos for video or printer. Normally we would use about 75 to 200 dpi. Perhaps 200 dpi for printing on photoquality printers, and more likely 100 to 150 dpi for video monitors, and much of the time, 300 dpi would be unnecessary overkill and waste and pain. But it's not without exception, and the most common exception would be to create large images for photo-quality printers (more in the Printer Resolution section).
I would suggest that 200 dpi or 300 dpi is often HIGH scanning resolution. You must ask yourself "What am I going to do with this image? What does the output device need? Can it make use of a huge image?". Except for a few special purposes, and except for Line art, more than 200 dpi can often be pointless and painful, because our output devices are not likely to be able to use more.
Part of my goal here is to point out to newbies that it is quite reasonable to scan photo prints at "as low as possible" resolution, instead of "as high as possible". "Possible" depends on the job to be accomplished.
We will speak about graphic file formats in a following section, but I would be derelict in my duty if I did not offer my opinion that it is absurd to scan a huge image supposedly "for quality" and then archive it in JPG format so the file will be small. These are conflicting goals, you either want maximal quality, or maybe not in every case. See the File Format section for advice about NOT storing your only master copy as a JPG file. JPG format is wonderful for many purposes, but archiving maximum quality is not one of them. A printer file may be an exception, and certainly web pages and email are exceptions, but I did use the word "archive" above. You would make compressed copies for purposes where size matters more than quality, but you would keep your one valuable master copy squirreled away somewhere safe as a TIF file. Each concept does have its purposes, but it doesn't make sense to use a huge but low-grade image for your master copy. You can't have both, it's a law, and they will get you. <grin> It is a very common mistake, but you'll either want the best image, like archive quality, or a small file, like for email or a web page.
The best way to reduce file size is to reduce resolution to a useful amount.
If you do have a good reason to work up near 300 dpi with color images, you'll want a lot of memory. A 300 dpi 8.5x11 inch color image is 25 megabytes!