The accepted answer to the question C++ Library for image recognition: images containing words to string recommended that you:
How would I do this... I was under the impression that DPI was for monitors, not image formats.
OCR software is typically designed to work with "normal" font sizes. From an image point of view, this means that it will be looking for letters perhaps around the 30 to 100 pixel height range. Images of much higher resolution would produce letters that appear much too large for the OCR software to process efficiently. Similarly, images of lower resolution would not provide enough pixels for the software to recognise letters.
DPI makes sense whenever you're relating an image in pixels to a physical device with a picture size. In the case of OCR, it usually means the resolution of the scan, i.e. how many pixels will you get for each inch of your scan. A 12-point font is meant to be printed at 12/72 inches per line, and an upper-case character might fill about 80% of that; thus it would be approximately 40 pixels tall when scanned at 300 DPI.
Many image formats have a DPI recorded in them. If the image was scanned, this should be the exact setting from the scanner. If it came from a digital camera, it always says 72 DPI, which is a default value mandated by the EXIF specification; this is because a camera can't know the original size of the image. When you create an image with an imaging program, you might have the opportunity to set the DPI to any arbitrary value. This is a convenience for you to specify how you want the final image to be used, and has no bearing on the detail contained in the image.
Here's a previous question that asks the details of resizing an image: http://stackoverflow.com/questions/353039/how-do-i-do-high-quality-scaling-of-a-image
I think the more accurate term here is resampling. You want a pixel resolution high enough to support accurate OCR. Font size (e.g. in points) is typically measured in units of length, not pixels. Since 72 points = 1 inch, we need 300/72 pixels-per-point for a resolution of 300 dpi ("pixels-per-inch"). That means a typical 12-point font has a height (or more accurately, base-line to base-line distance in single-spaced text) of 50 pixels.
Ideally, your source documents should be scanned at an appropriate resolution for the given font size, so that the font in the image is about 50 pixels high. If the resolution is too high/low, you can easily resample the image using a graphics program (e.g. GIMP). You can also do this programmatically through a graphics library, such as ImageMagick which has interfaces for many programming languages.
"How would I do this... I was under the impression that dpi was for monitors, not image formats."
DPI stands for dots per inch. What does it have to do with monitors? Well, we have a pixel made of three RGB subpixels. The higher the DPI, the more details you cram into that space.
DPI is a useful measurement for displays and prints but nothing useful... in fact, nothing for image formats themselves.
The reason for DPI being tagged inside some formats is to instruct the devices to display at that resolution but from what I understand, virtually all ignore that instruction and does its best to optimize the image for a particular output.
You can change 72 dpi to 1 dpi or 6000 dpi in an image format and it won't make a difference whatsoever on a monitor. "Upsize/downsize to 300 dpi" makes no sense. Resampling does not change DPI either. Try it in Photoshop, uncheck "Resample" when changing the DPI and you'll see no difference whatsoever. It will NOT get bigger or smaller.
DPI is totally meaningless for image formats, IMO.
If your goal is OCR, DPI makes sense as the number of dots in your image for each inch in the original scanned document. If your dpi is too low, the information is gone forever, and even bicubic interpolation is not going to to a brilliant job recovering it. If your dpi is too high, it's easy to throw away bits.
To get the job done; I'm a big fan of the netpbm/pbmplus toolset; the tool to start with is pnmscale, although if you've got a bitmap you want to consider related tools such as pbmreduce.