There are some photographers like Michael ackerman, Daido Moriyama, Igor Posner, Jacob Aue Sobol, who shoot digitally but some also analog who very often achieve to bring a nice looking grain in their images. So, Is it possible to produce nice looking analog grain digitally in Photoshop or other applications?
There are multiple solutions for that:
On a vanilla factory Adobe Photoshop without any plugins:
What I use to do is to create a 50% gray layer ( rgb(128, 128, 128) ) that I put in one of the following blending modes: Overlay, Soft Light or Hard Light, doing so your layer won't have any effect because those blending modes are 50% gray centered. Then I do a 'Add Noise...' filter, don't put it too strong, 50% is a good start, you will be able to dial it down afterward anyway, distribution is a matter of taste.
Then the trick is to adjust the grain size is to blur your layer however blurring everything at the same value would result in poor uniform appearance, that's why you want to blur your red, green, blue channels with different values, you can blur your blue channel more than the red or green for instance.
For more control you can even have the red, green, blue grain on different layers so that you can dial their intensity easily. You can even put that in smart objects if you need even more control.
From there it's very easy to create your own actions to simulate various film stocks.
If you can buy plugins:
One I use all the is "Red Giant - Magic Bullet Photolooks", it does a lot of things more than grain, but it's film grain node is quick and easy to use. I found that while searching for a dedicated plugin: Power Retouche Film Grain, it looks to have a lot of controls.
If you have access to compositing applications:
An interesting take is to scan an empty film frame and use this noise frame as an overlay. In the following photo, I have moved the grain layer halfway to the right so that you can see the effect more clearly:
This is how the grain looks in detail (you probably want to open the image to skip the compression and resizing artifacts):
This looks very nice and natural, as you get all sorts of small blemishes and “grain islands” that appear on film. On the other hand, the grain is always the same on all your pictures, unless you shuffle the overlay with each use somehow (rotate, shift, etc).
You can add grain to an image using Adobe Lightroom if you want to add the grain digitally during post processing.