Is it ever appropriate to decrease or increase the resolution of an image in Photoshop? Why or why not?

Yes and no. I work with large format printing, so I am constantly having to increase photo resolution. One trick I use for increasing the resolution of an image is to increase the image size by 125% using the bicubic smoother option. Then, I increase it once more by 125%. Then, I use the sharpen filter. This can usually be done only once or twice before the image becomes too blurry or pixelated.

As for decreasing resolution, be sure to use the bicubic sharper method for a cleaner looking image.

Resolution = Quality of an image.

mainly we differentiate the image quality and usage based on the resolution. resolution can be categorized in to DPI / LPI / PPI .

DPI- dots per inch
LPI- lines per inch
PPI- pixels per inch

different resolution for different purpose

72- > system viewing purpose
72-100 > for web designing and web related images
300 and above > for printing purpose

these are the basic resolution sizes on an image. Increase and decrease in resolution will effect the pixels and quality of an image

Yes...increase a bit, as per Mr. Wright, if you need to, and decreasing, no problem...HAVE to do it all the time for web, for loading ease and speed, even in this day of cable modems.

As to why...when I taught HS students photoshop I explained resolution, or as I called it, 'old-school style' just for increased understanding, and then went back to calling it resolution: bit-depth...it's like the x & y values / length and width, but it's the depth, the z, the "thickness" of the image, how many pixels are behind each one of the pixels in the image...for some needs, like web, you can and need to slice it thin; for other needs, where you stretch it out, even if it's thick, you only have a certain number of pixels to play with in the front layer, and if you stretch 'em out, it will look pixelated.

Absolutely.

I usually decrease my file sizes if I'm putting them on the web.
I usually decrease the pixels if I need a larger picture. - I only do that if I have enough wiggle room. Nothing below 200ppi if I'm going to print it.

I would never try to increase the resolution without decreasing the size. It will look horrible and everyone will think ICK, what a bad photographer!