What are some soft skills everyone should try to develop? Why? When and how can they be applied?

Good ones here already. I'll toss in a few more that are my own opinion, of course...

Boundaries. Have some. Know when not to interrupt, what not to ask, what not to share, when not to touch, and what NOT to say in certain social settings. If you're not sure, just don't.

Honor elders. Everything from shutting up when they're talking, not correcting them in a harsh manner, or giving them your seat in a crowded room or on public transportation, to simply holding the door for them. Also, call them Mr., Ms., or Mrs.

Know when to speak, and vice versa. One of the wisest pieces of advice I received from an extremely successful entrepreneur was never to speak first at the table or in a room full of people whose experience or in his words "stack" outweighs yours. The risk of sounding completely foolish is high. Assess the conversation first. Listen first, and the likelihood your response will be informed, and insightful is much higher.

Remember first names. Use mnemonics, use whatever you can, but make effort to do it. It sets you apart from the rest.

Don't miss weddings & funerals. This is hard to execute, but the older I get, the more I realize how important these events are. I literally break my neck and make every effort I can to attend a funeral or a wedding of anyone who is even remotely important to me. You'll find the trickle down effect of this shows others around you that you value relationships and honor people.

On occasion, and when appropriate, use Sir, and Ma'am. I miss hearing this with this up and coming generation.

Eliminate false humility. Learn how to talk about personal accomplishments in a social setting without sounding arrogant, or projecting insecurity or false humility. People like to know more about you, so when they ask, don't downplay yourself, but also don't uptalk yourself. Just be.