When shooting black and white film, I almost always push it. It does depend on what film it is of course, for example I do not normally push Fomapan, because I really like how it looks as is. I like to push other films because of the higher contrast and increased grain pushing film inherently causes. For a long time I would shoot pretty much only Kodak Trix 400 at either 800 or 1000. It was what I had found I liked and I saw no reason to not use it. A few months ago I bought the Monochrome Bikkuri Film Case from JapanCameraHunter, and inside it came with a number of black and white films I had not used before. It had Ilford HP5, which I think is the film I was using when I was in the darkroom club as a kid at school. One thing stood out on this film in particular: it had a check box to say if you shot it at 400, 800, 1600, or other. So, with my rolls of HP5, I decided to try each ISO out.
This is the ‘normal’ ISO for this film. It looks pretty standard in my opinion. It is grainier than other films I have used at 400, but it fairs well as just a standard 400 black and white film. I used it at a hanami, where one has a picnic under a sakura tree in Japan, and I like the results. You can see them below.