One thing blogging and good copywriting share is a conversational style, and that means it's fine to fracture the occasional rule of proper grammar in order to communicate effectively. Both bloggers and copywriters routinely end sentences with prepositions, dangle a modifier in a purely technical sense, or make liberal use of the ellipsis when an EM dash is the correct choice—all in order to write in the way people actually speak.

Your vs. You're:

This one drives me insane, and it's become extremely common among bloggers. All it takes to avoid this error is to take a second and think about what you're trying to say.

"Your" is a possessive pronoun, as in "your car" or "your blog." "You're" is a contraction for "you are," as in "you're screwing up your writing by using your when you really mean you are."

It's vs. Its:

"It's" is a contraction of "it is" or "it has." "Its" is a possessive pronoun, as in "this blog has lost its mojo." Here's an easy rule of thumb—repeat your sentence out loud using "it is" instead. If that sounds goofy, "its" is likely the correct choice.

There vs. Their:

"There" is used many ways, including as a reference to a place ("let's go there") or as a pronoun ("there is no hope"). "Their" is a plural possessive pronoun, as in "their bags" or "their opinions." Always do the "that's ours!" test—are you talking about more than one person and something that they possess? If so, "their" will get you there.

Affect vs. Effect:

"Affect" is a verb, as in "Your ability to communicate clearly will affect your income immensely." "Effect" is a noun, as in "The effect of a parent's low income on a child's future is well documented." By thinking in terms of "the effect," you can usually sort out which is which, because you can't stick a "the" in front of a verb. While some people do use "effect" as a verb ("a strategy to effect a settlement"), they are usually lawyers, and you should therefore ignore them if you want to write like a human.

The Dangling Participle:

The dangling participle may be the most egregious of the most common writing mistakes. Not only will this error damage the flow of your writing, it can also make it impossible for someone to understand what you're trying to say.