If someone is in danger of life and limb, we are forbidden to stand by doing nothing if it is within our ability to help. If someone is drowning in a river or being attacked, taking video on your cell phone is reprehensible. Put the phone away and help, or at the very least use it to call 911! (Not standing idly by requires us to act within reason. If you can’t swim, no one expects you to jump in and drown, too. If you’ll get yourself killed, call the police.)
Related to this is not to withhold testimony that could save someone in a court case, even in a financial matter. If you have pertinent information and don’t come forward… well, that’s kind of a jerky thing to do.
Our verse here ends with the words, “I am God.” A person has plausible deniability. He could say “the rapids were too much for me!” or “the robber was armed!” God knows, however, whether a person truly lacked the ability to help or merely didn’t feel like it.
This mitzvah applies to both men and women in all times and places. It is discussed in the Talmud in tractate Sanhedrin on page 73a. It is codified in the Shulchan Aruch in Choshen Mishpat 426. This prohibition is #297 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #82 of the 194 negative mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.