Should you care about what others think about you at work?

Should you care what others think about you at work? Some of the most successful people I've seen could care less what others think of them. I'm jealous of those people.

My thought: don't seek approval, but seek respect.

- If your decision is based on fear of dissapointing someone, you're chasing approval.

- If your decision is based on what's right and necessary to achieve your goals, your building respect.

What do others think?