Rules

Use proper grammar and spelling.
This is a big one. Now, of course, we all make mistakes from time to time, but when you completely disregard spelling and grammar, it is a major issue. It is difficult to understand a character if they are talking in chatspeak. It is especially bad if you are roleplaying without punctuation, and we must decipher between two separate sentences that someone wrote together.

For example: “He was going to call her but he didn't have any idea what to do he called her later and asked if she could come over”

How can there be a serious discussion and understanding one another if this happens? We have the beauty of spell-checking; please use it.

Do not God-Mod.
If anything (or most things) cannot defeat your character, there's a big problem. To my knowledge, the majority of characters are not immortal, so do not treat your character like they are a god that cannot be touched, or they fight better than anybody else. Try to come to an understanding with your fellow roleplayer(s) about your characters' abilities and try to reach a compromise.

For example, my friend and I decided to make in a duel between our characters, to have mine win at physical combat, and hers at magical abilities. Do you see how that evens out?

Do not write out the follow-through of an action that your character made.
This happens a lot in roleplays and it is quite frustrating. This is taking too much control over what is going on in the story. For example, let's say your character pushes mine because of something mine said. Taking too much control over this would present itself in this manner:  

"Avelyn shoved Ikkesh so hard he crashed into the wall and he fell, unconscious."

Don't do this. You can say, "Avelyn moved to shove Ikkesh hard, disgusted by what he said." And leave it be. Write it as an attempt, not a follow-through. “He swung his knife at the strange man,” NOT: “He stabbed the strange man in the chest with his knife.” Let your fellow roleplayer(s) determine what the result of the action is before you go ahead and fill that in. Type an action, but let your friend do the follow-up. If you do not allow your friend to make the aftermath connection, you are controlling too much, and therefore your roleplay will just be about what you and your characters want to do without any mutual benefit between roleplayer(s).

No Mary Sues/Gary Stus.
This is a dead horse in and of itself, but I'm going to briefly beat it for the 15 billionth time. Do not have a Mary Sue or Gary Stu character used in a roleplay. I'm tired of seeing characters that are loved by everyone or are too emo and hated by everyone. There are also other versions of Mary Sues and Gary Stus, but I won't go into them. If you are concerned that your character(s) might be a Sue/Stu, discuss them with your roleplay partner(s) and try to work out the kinks.

Of course, no character is going to be 100% exempt from all clichés, but it is good if there are as few as possible.

Keep character secrets among the characters that are involved with it.
This one is more common than you think. Let’s say Avelyn tells Ikkesh a secret that she is from another world. The problem comes in if other characters, like Fanchon and Orphelia, also learn about this as well, when neither Avelyn nor Ikkesh told them. If Fanchon starts to pick up that she’s from another world, it had better be based on what he has experienced of her, not what the roleplayers now know. Orphelia shouldn’t come in and then immediately start asking Avelyn questions like, “You know, you don’t seem normal enough to be human.” If she never thought that idea before Avelyn telling Ikkesh the secret, don’t have her suddenly switch her position. If no one spilled the beans to other characters, watch carefully.

Differentiate between what you know and what your character knows; that is vital.

Don’t flirt with a character immediately and expect reciprocation.
Unless your character is an outright pervert, you shouldn’t have a character immediately come onto your fellow roleplayer(s)’s characters. They just met; do you expect relationships to be founded in a few minutes? Also, don’t assume that even after a while that all of a sudden your two characters will get together to be a couple. If your partner and their character don’t want a part of it, don’t try to force it onto them.

Keep the roleplay PG-13 unless there is clarification otherwise.
Nothing worse than starting to have sexual encounters come up or extremely violent situations happen when you thought you were in for a roleplay that had just some violence and minimal romantic affairs. Be clear with your fellow roleplayer(s) about what kind of roleplay you are planning on having. Be open if your partner(s) is not willing to have a certain roleplay even if you are. Don’t force anything if they are not comfortable.

Be sure to cement what form of roleplaying you are doing.
The two kinds of roleplaying that are most often done are script and story style. Below are examples to show you what I mean:

Story Style
Evelyn grinned and folded her arms casually. ‘He’s odd,’ she thought to herself. She asked, “So, what is your name?”
Script Style
Evelyn: *grins and folds her arms casually. ‘He’s odd,’ she thinks to herself* So, what is your name?

Of course, set up for some of these things can change (some people like to put thoughts outside of the asterisks, etc.) but so long as you and your fellow roleplayer(s)s are on the same page, all is well.

Do not be afraid to ask questions.
If your fellow roleplayer(s) has their character say or do something that is not clear, or you are confused in another regard, let them know. The roleplay cannot be productive and fun if you are lost through half of the story, so save yourself irritation and ask.

Give your fellow roleplayer(s) adequate time to respond to your posts.
Oftentimes, if the person is busy or just very delicate when it comes to their writing, it may take a while for a response. Overall, be patient. Allow time for a reply to be made and don't rush it. Taking turns in roleplay helps a great deal for a one-on-one situation. For a group setting, be sure all of your partners are up for taking turns and determine an order, such as alphabetical. Turns are a sure-fire way that everyone has their post matter.

Do not bring up facts about your character in an inappropriate scene or time.
It would not be suitable in a casual conversation or trip to have your character speak of their troubling past. Remember, all the edges of your character's story and personality should not be exposed in-character so soon (out of character is a different story, when you're telling your roleplay partner about your character so they get a feel for what they're going to be dealing with).
Keep in mind that your fellow roleplayer(s) is attempting to show and develop their character as well.

Planning roleplays can help the experience.
You can take turns having one roleplay in your world, with the next being in your friends' world. Spending time mapping out some of what will happen can add to the fun as well. Take time to plan which characters you will use. Use appropriate characters for certain situations.
It is not a necessity to plan out a roleplay, but for ones that might be helpful for you to develop your character and also to perhaps roleplay through a section of your story that might need work, planning is very important.

Try to keep your posts from being too short or too lengthy.
There is a middle ground of posting that I think everyone would want in a roleplay, as I have seen people complaining about the two extremes of this. There’s the person who posts one-liners that doesn’t do much for the story. Myself, I’m not against one-liners if they work, because they can. But if hardly any effort is put into them, there is a problem.

There is also the issue of the person who writes too much. Now, if you are just describing a new place, item, person, etc. I can understand, or you’re writing a long action. However, if the description is starting to talk about things that are not relevant to the story, or they’re just overall getting too far into detail, then I think it’s time to pedal back.
For example, when explaining the physical characteristics of your character, saying, “Her eyes were violet in color,” is generally better than saying, “Her eyes were a vibrant bright color of violet that sparkled amazingly in the sun and drew in others as they stared into it. They were irresistible to men and women alike in a way that could not be described by words.” Say the facts, but do not create an analysis of them; leave that up to your fellow roleplayer(s) to decide.

Don't take over the character(s) your RP partner is using.
This is very rare, but it does happen in some reps. If you want an RP to be fun and productive, don't overstep your bounds and take control of a character that your partner is supposed to be writing for. Unless they have permitted you to do so, only use the characters you agreed to use. If you did not make a plan before you started, be sure to ask before you jump the gun.