IMHO, pushing for one stop is a waste of good film. Pushing for two stops can give very good results. The biggest consideration when pushing is the type of lighting.
To define "pushing": exposing as if your film is faster than it is, and developing longer than normal to compensate. For example, shooting Tri-X 400 as if it was a 1600 ISO film. It's not, so you lose some ability to capture the brightest lights and darkest shadows. But at 1600, what you lose is minimal in most scenes. The reason you do it varies. Most commonly, it's because you can't otherwise get an aperture and shutter combination that eliminates camera shake and/or subject movement blurring, or you want the "look" - you [/i]don't want[/i] to capture every tone the film is capable of capturing.
Bar scenes are very often quite contrasty, and any push becomes obvious as lighting turns to white-out bursts and shadows disappear into inky black. The effect can be quite dramatic and pleasing. Snow-covered streets and fields work very well, with a full range of tones on the negative as the reflected light from the snow illuminates more evenly. The negative isn't showing the full range it is capable of, but it doesn't need to look like a block print.
Exposure is important - know that a light bulb is going to appear as a globe of white when pushing, and the greater the push, the more pronounced the effect. If you don't expose for the shadow details specifically, they will be lost in blackness in most cases because the film simply didn't get enough light from them. It doesn't matter how long you let it sit in the developer, unexposed film is unexposed film. And things like streetlights lose all shape and detail because everything above a certain point becomes blank white on the print.
That said, pushing is a very useful tool. It lets you capture scenes that would otherwise not be possible. It also lets you capture a scene as *you* want it to look, rather than as someone else might have taken it. It's a creative tool.