Wow! didn't realise this was such a dangerous topic, so at great risk will add my 5 pence worth :)
ISO really matters with film - the lower the ISO the finer the silver grains, so the better the resolution. Increase the grain size, will allow lower light levels to be captured because grains are bigger, but with less grains the resolution will be less. With enlargements from film there is a very noticeable difference between same-size enlargement from ISO100 and ISO800 for example - and the fall off is non-linear (inverse square law applies to grain size where double the size of the grain for more sensitivity reduces the area coverage and hence resolution by a factor of 4.)
With film of course you fix your ISO for the next 20 or 36 frames the moment you put a film in and you can only adjust Aperture and/or shutter speed to control exposure.
One of the greatest benefits of digital cameras is that many of the constraints of film no longer apply in the same way and ISO is an example.
With a digital sensor the pixel size and total pixel count remain the same no matter what ISO is selected. Digital ISO is therefore an electronic adjustment of sensitivity. Make it lower and it allows more light to be 'gathered' for given Aperture and shutter speed, and vice versa.
So the resolution doesn't change as 24Mpx is still 24Mpx. The downside is that increase ISO to very high values and the 'gathered' light is insufficient to determine exactly what the pixel is recording - is it red , blue, green etc and we get Noise
The best analogy I ever read was visualise each grain or pixel as a cup:
with film we change the surface area and hence the volume of the cup, and pack more or less in. The'volume' of light captured changes accordingly and so does the resolution depending how tightly packed they are.
With a digital sensor the surface area never changes, we just change the 'volume' of the cup. Resolution is unchanged, but quality of recorded light increases or degrades.
Who cares?
I use most of the camera settings - aperture and shutter priority, and manual as needed.
Typically I use Aperture as I want to control DoF on a landscape or a portrait. I keep an eye on shutter speed to ensure it is reasonable to reduce camera shake (using the rule of thumb it should be equal to at least 1/focal length of lens as a starting point) and let ISO take care of itself.
Similarly with fast moving subjects - birds, aircraft etc I fix shutter, and keep an eye on aperture.
I only use manual when A or S priority doesn't give me what I want - a 20 sec f2.8 exposure for a night scene; an aircraft if I want motion blur in the propellers, etc. In these cases the need to specifically set aperture and shutter speed in manual mode, means I need to set ISO also to get what I want
My view is a modern camera is not unlike a car: 50 years ago (from personal experience) you had to use the choke, accelerator, gearstick, clutch, wave your hand out of the window to indicate, to get from A to B. Similarly a camera - you HAD to understand the relationship between aperture, shutter speed and ISO (or ASA as it was then.) Nowadays the modern digital camera can do as much as or little as you want. My greatest challenge has always been composition. A modern digital camera is almost liberating in that it frees me to focus on the most difficult part (for me.)
Or as an renowned expert I once saw said 'always using a digital camera in manual mode is a bit like having a car and running alongside'
Please flame courteously