The word myself just seems like an awkward word. Seems like “me” or “I” would be more appropriate every sentence I can think of. Is it a real word?
It’s a reflexive pronoun. You use it when you’re the subject and the object.
“I like myself.”
In this sentence myself could still be replaced by “me” and make sense. An example in which neither “I” nor"me" could be substituted is
“I’ll do it myself.”
Here ya go, this explains it better than I can:
Source: Pronouns | Pronoun Examples and Rules
or:
Source: http://grammar.quickanddirtytips.com/myself-
grammar.aspx
I myself don’t usually worry about the proper or improper use and will usually try to find a way to say “me” instead so that the sentence doesn’t get overly awkward. 
ETA: Another sentence in which “myself” is correct and could not be replaced with “me” is: I’ll do it myself.(as noted above) Basically anywhere you would use “yourself” if referring to someone else, “myself” is appropriate. "
This nonstandard (wrong) usage makes my ears bleed. Unfortunately, it is catching on and I’m sad to say that it will likely become commonly accepted within the next decade.
The same with its/it’s. Even allegedly educated people don’t know when to use the apostrophe and the usage will evolve to the point where the apostrophe is always used regardless of the meaning.
Similar and correct usage as a way to indicate stress, especially when there’s a difference to be noted: “You’re a Democrat? I’m a Republican, myself.”
I find that many people do not like to use the word “me”, because they are afraid they will sound low class, e.g., “Me and Johnny are going to the store.”. So they use “I” and “myself” when “me” is the proper word to use (which makes my ears bleed too).
Examples:
You have been so kind to my family and I.
Johnny and myself are going to the store.
Please give it to Johnny or I.
And yes, I hear all of these usages on TV and in person ALL THE TIME.
Don’t get me started on it’s/its. How hard is it to substitute “it is” to see which is correct???
Where I live, enthusiastic use of reflexive pronouns is a feature of the local dialect. “How’s himself/herself?” means “How’s your significant other/relative/co-worker/boss”, “it’s up to you” becomes “it’s up to yourself”, etc.
I myself rarely use it.
The OP’s problem is that the horrible improper use, where people use the word instead of “me” just to sound high-class (and end up sounding like uneducated morons), is becoming so common that it’s taking over. My old boss at my first job out of high school did this on a daily basis, and every time it made me cringe. But don’t worry – she’s dead now.
–Cliffy
“When I think about you, I touch myself.”
I went on a similar rant on the “…banned from using whomever” thread. I hear ya on the misuse of "I’. It is one of my absolute grammatical peeves. The most egregious use I have ever seen or heard was on another message board where the poster used this in a sentence, “My roommate’s and I’s apartment…” shudder
The more common misuses though are becoming really too common and I worry about the state of the language in the very near future. 
I cannot tell you how many times I have heard the phrase “between you and I” in just the last day or two…It makes me crazy.
Although you could just drop the last word and the sentence means exactly the same thing:
“I’ll do it.”
The word is in my experience used constantly. It took me a couple of seconds of googling to find it being used in 1855 (by Walt Whitman, no less) and I don’t doubt that it goes back waaaaay further than than. I also don’t doubt that it’s been in continuous use since. There are at least 202 million pages on the internet that use the word at least once.
I’d be very interested in the definition of “real” you might be using that you would question whether “myself” was a real word.
“Allow myself to introduce… myself.”
Sure, but you potentially lose emphasis.
i.e. it’s really someone else’s problem but you’re highlighting the fact that it’s specifically you who needs to get it sorted.
A - to the freaking - MEN!
“Me” is a totally fine word. It pleases me to hear it used properly.
No, that sentence doesn’t mean exactly the same thing. Your sentence means the speaker is willing to shoulder the task. The original sentence means the speaker’s spouse is not getting oral sex for at least a week.
–Cliffy
please allow me to introduce myself i’m a man of wealth and taste…
No, it’s not quite the same thing. To illustrate, suppose I go to a shoe-repair shop. If I say to the person at the counter, “Will you fix these shoes?”, the person has the option of passing on the work to an assistant. If I say, “Will you fix these shoes yourself?”, then I am asking that the person fix the shoes personally, and not delegate the work.