This is key, be it about the plot, your partner's limitations, or your partner in general. Discuss plot points, action to be taken, and whether or not the RP is working for you. You should both be happy and comfortable with what you're writing.
Respect each other's ideas.
Respect each other's time.
Respect each other as people.
There is another person on the end of your computer/phone screen that is taking the time out of their day to write something to you. Respect them.
Roleplaying is a collaborative effort. Offer ideas to encourage the growth of the plot; remember details within the plot to make character interactions more believable. Don't take over, but don't expect your partner to take the lead, either. Work together.
3RD PERSON, PAST TENSE
Most roleplays are written in 3rd person, past tense with an omnipresent perspective. Unless you have discussed with your partner writing in a different style (ie; 1st person, present tense), it is safe to assume that this is what is expected of you.
While some mistakes are alright, you should still put some effort into keeping your sentence structure and spelling correct. If you have to run your work through spell check, do it. It's easier to read. Remember: typos are okay, chatspeak is not.
NO GOD MODING, POWER PLAYING
God moding refers to invincible, incredibly powerful characters that cannot be harmed or defeated. Think of them as Superman without kryptonite. Power playing refers to controlling your partner's character, often without your partner's consent. Both are frowned upon in the RP world.
NO MARY SUES, GARY STUS
Make believable characters: it's that simple. Don't make a character that is inherently perfect, can do nothing wrong, and is constantly the center of attention for an inexplicable reason. It's boring, unrealistic, and annoying to interact with.
SOMETHING TO REPLY TO
Write something that your partner can interact with. It doesn't matter if you're the type to write a single sentence or an entire chapter; length means nothing if you don't give your partner something to reply to.
Don't leave your partner hanging if you're going away or no longer interested in the roleplay. If you're going to be gone for a few days and won't be able to reply, let them know. If you're no longer interested in writing with them, politely say so. Don't just disappear.
This may seem like a silly rule, but it's true. If you're not having fun with your roleplay, then you're doing something wrong. It shouldn't feel like a chore or something you have to do. You should be excited to read and write a new reply from/to your partner.