Always try to get closer, unless you are limited by the surroundings or constrains of your camera/lens.
My reasons to crop:
1) Most of the time when shooting street, I don't have a lot of time to compose my shots before the subject disappears. As I practice, my composition gets better & faster but one thing I find it impossible to get it right shooting handheld is to get my pictures 100% straight. I almost had to straighten, with slight crop, to all my street photos.
2) Realize there are distracting elements in the background & is too difficult to photoshop away
3) Cropping to try & make a lousy composition work.
Cropping is almost unavoidable for me. Lens correction alone will cause a bit of cropping. Adjusting for verticals of buildings will also need to crop somewhat. Changing aspect ratio will again need to crop. Sometimes I am anal about the positioning which cannot be precisely framed as I desire when viewing through live view so I shoot a bit more. I crop very generously if necessary. After all, only the end product counts and since I am not a pro (meaning no need to answer to paying customers), doesn't matter to me as long as it looks good on monitor. I always try to shoot with some excess spaces to make room for such adjustments in post.
Cropping, or removing certain portions of a photograph, has been around since the beginning of photography. In the digital photography age it is easier than ever to use this technique to bring about stellar results from your photographs.
If I edit, most likely cropping is the minimum I will do. Serious cropping will happen when my tools cannot give me that required zoom. I feel cropping is not cheating but an added value to photography.