1. Keep your cool - No matter what someone else may be writing, how irate or abusive they're being, do not sink to their level. If you feel yourself becoming angry - and don't we all at times - walk away from it for a few hours and come back with a more relaxed head.
2. Never insult your readers' intelligence - Just because someone disagrees, doesn't make them stupid. In all honesty, of course, they might be stupid, but you can't make that judgement based on a three sentence comment.
And, if you resort to insinuating or outright saying that a commenter is 'stupid' it says far more about you than it does about them. And, just in case you were wondering, what it says ain't pretty.
3. Subscribe to Voltaire's school of thought - "I do not agree with what you have to say, but I defend to the death you're right to say it." As long as someone is expressing themselves in a reasonably polite manner, there's no need to rubbish their opinion.
For example, if I'd written an article about the oblate spheroid nature of the Earth and someone said they believe the world is actually flat, that's not harming me, so there's no point in starting an argument. As Salt 'n' Peppa's 'None of Yo Business' teaches us, "opinions are like (expletives) and everybody's got one". If you intend to go around telling everybody, who disagrees with you, that they're not entitled to an opinion, you'd be better off in Stalinist Russia...As long as you are Stalin, of course.
4. Pick your battles - As mentioned above, there are some things that are just not worth getting your panties in a bunch over. Other things, however, are worthy of your time. As always, though, convey yourself in a respectful way.
Always remember, your success as an online writer is as much about your online persona as it is about your talents as a writer. So, don't put those unflattering colors on display.
5. Always respect other's cultural or religious beliefs - Personally, I don't believe in a God, but it would be arrogant and obnoxious of me to tell others that they're wrong to believe otherwise. When it comes to matters of faith or perception, as long as nothing offensive is being written by your readers, they have every right to hold those beliefs.