Of course, there's the standard definition: A feeling of deep admiration for someone or something elicited by their ability, qualities, or achievements. That's interesting. Most of the time when I hear people spouting off about respect, it usually has very little to do with this definition. It's more of a selfish standpoint of "My respect is earned..and you should be honored to have it." Um.. No. If you're using that attitude with me, you OBVIOUSLY don't hold any respect towards me to begin with.
With the technical definition aside, I'm going to focus on respecting people with whom you are in a relationship with. Now, this relationship can be a friendship, a partnership, an intimate relationship, even a working relationship. In order for a relationship to work completely, there must be a level of mutual respect. Respect is very rarely equal, but it certainly needs to be present on both sides in order to have a successful relationship. When there isn't any respect, trust goes out the window, and resent moves right in.
I see respect in a different light than a lot of people, so I'll share my thoughts on it here. Respect is more than just a word to me, it's a culmination of several things that, when put together, represent a high regard for the person with which you're dealing. I like to use the word respect as an acronym for a variety of different actions and thoughts; when put together, show the other person you truly do respect them.
R: Responsibility. In a respectful relationship, you take responsibility for your actions and your words. When you do something that hurts the other person, you take responsibility for it and apologize. Only then can you hope to move forward with the relationship.
E: Engage. No, I don't mean engage as in married (gah!). Engaging the other person in your thought process, your decision making, and other aspects of your life as necessary is an excellent way to show your respect for them. If you continue to make all the decisions on your own (especially ones that involve the other person) you are immediately negating their thoughts or feelings on the subject, and in return; proving that you don't respect their wishes or beliefs.
S: Selfless. Be selfless; give yourself to others (to the extent that you can). Remember that the world doesn't revolve around you and that in a strong relationship, it's up to you to keep the feelings, desires and needs of the other person in mind when you act on something.
P: Purge. I know, it's an odd word, but it's important to purge yourself and your relationships of negative energy. Get rid of the "bad" stuff.. if you respect someone, truly respect them, and they have offered an apology for something they have done wrong, forgive them. Purge it from your relationship and don't bring it up again. Respect is about moving forward, not living in the past.
E: Earn. It's said all the time... respect is earned. I believe this to a degree, but I think people take the concept a little too far sometimes. That being said, I think that the best way to earn respect is to respect others in return. Earn respect by showing others that you're a good, compassionate, thoughtful person.
C: Care. Care about others, and show you care. Don't just assume that they know and don't just tell them - words can be very empty sometimes. Put your words into actions and SHOW them you care. Let them lean on you. Lend an ear, or a hand up, or help when they need it. Help them laugh when they are down and cry with them when they are hurt.
T: Truth. Tell. The. Truth. All the time, without fail. If you respect someone, you don't lie to them -- end of story. Lying to someone is the ultimate betrayal of trust; and just proves that you don't respect them at all.
So, there it is in a nutshell -- take it for what you can get out of it. But remember this - respecting someone and showing that respect to them is the single most important part of a relationship. Every relationship.
Be at peace with yourself, and you'll be at peace with the world.