The world moves fast. Email can be transmitted in moments, practically everything has a drive-through window, and the moment you hit "send" on Facebook your words are out there for everyone to see -- you might even get a comment or a "like" within seconds. Sometimes, it's necessary to use abbreviations (after all, Twitter only gives you 140 characters). But you should think twice, and edit heavily, before you put them in your book. Don't let abbreviations ruin your work.
Common abbreviations crop up in writing all the time. They're included in online articles, they're used on blogs, they're great for Twitter and other social media sites where space is limited. It's so easy to use them, you might never even think about it.
But you should, because even everyday abbreviations should be absolutely left out of your books. Have you ever actually heard someone use one in conversation? When was the last time you said e.g., when you meant for example, or i.e. for that is? People do commonly say et cetera, but if they're doing it in your book it should presented spelled out and not as etc.
Using abbreviations in book writing, even the very common ones, looks lazy and unrealistic. People don't use them in speech, and you certainly should use them in your writing...well, for the most part. Like every good rule of writing, there are plenty of exceptions to this one.
Certain acronyms, which are definitely in the same language family as abbreviations, are used all the time in speech and in writing. PETA, MADD, NASA -- the list goes on. Your book could easily become cumbersome if you're spelling out People for the Ethical Treatment of Animals instead of PETA, and some readers definitely won't know what you mean because the acronym is much more common.
OMG and other acronyms that crop up frequently in social media are trickier, and still new enough that many standard style guides don't address them. People do commonly use text-speak acronyms in everyday conversation, particularly younger people, so if you're writing a book with teenagers and kids in it these common acronyms are going to crop up. Some writers spell them out phonetically (oh em gee, for example), but it's simpler to just use the acronym itself, and this will create less confusion.
Titles are commonly abbreviated, and most readers are comfortable with seeing this. Keep on using abbreviations for Mr., Mrs., Dr. and all the other common titles that everyone abbreviates in writing. The exception to this is when the name isn't attached to the title. If my character says Doctor, what should I do? the title should be spelled out; but it's fine for me to write Dr. Green, what should I do?
When I'm writing in my notebook or making a notation on my to-do list, I might write "Jul 4" or "Aug 8" -- but I'm not ever going to do that in one of my books. It's all well and good to use shorthand when you're writing to yourself, but not to an audience. Don't abbreviate your dates unless you're specifically quoting something a character has written down (for example, Laurel had written "Mar 12" at the top of the page).
Text Messages, Emails, et al.
Speaking of stuff that characters are writing down, you may have the occasion to include emails, text messages and similar stuff in your book. When this is the case, it's more than okay to write with abbreviations, acronyms and even misspellings because that's how people write their texts and emails. Always make them authentic, and to heck with the rules. Again, and I cannot stress this enough, realism always trumps in writing.