Myself, I don't see a problem
It's grammar quiz time. Which of the following uses of myself are acceptable?
1. "You seem like a better version of myself."
2. "I just want to be myself."
3. "I haven't seen any myself."
4. "I myself haven't seen any."
5. "Myself, I haven't seen any."
6. "You would even say that to me myself?"
7. "There are two others here besides myself."
8. "He asked William and myself to do it."
9. "He was a man as big as myself."
10. "Myself, as director here, will cut the ribbon."
11. "William and myself will be there."
12. "Myself and William will be there."
13. "I asked myself what I could do."
14. "I directed all inquiries to myself."
The answer? It's not so simple! All of the above kinds of usage have been in common use in English for as long as there has been an English language (written records go back 1,500 years). And all of the above have been used by respected authors throughout the history of the language. But not all of them are considered acceptable in formal usage by everyone today! Indeed, even if you're not a fussy person, one or more of them may well sound wrong to you.
As recent generations have learned the simplistic rule "myself is a reflexive pronoun," other uses have come to be disallowed by the more prescriptive among us — not always with good justification. If you don't want to catch grief from grammar grumblers, you might as well know which ones are not looked on so highly now. Here are the different ways myself is used — and how acceptable they are now.
To mean "my self"
It would seem plain and simple that myself could mean "my self" — that is, "my being; my inner essence; my personality; my physical entity." Actually, the word wasn't originally myself; it was meself, just like himself and herself. The self was a pronoun, not a noun, and was used for self-reference for distinction or emphasis (you can still see this occasionally: "Bought a pair of tickets for self and companion"). But, with the help of the ambiguity of herself, people came to think of the reflexive as a possessive plus a noun form of self. So we now have myself — and ourselves, yourself, and yourselves, but himself and themselves.
Nonetheless, use of one-word myself to stand in for two-word my self is established and generally accepted: "You seem like a better version of myself" would not normally be objected to, and "I just want to be myself" is perfectly fine.
Once in my youth I was talking with a woman who had a background in journalism. "I myself—" I began, and she snapped, "'I myself' is redundant!" Well, she was wrong. Use of myself with I or me for emphasis is not mere redundancy; it emphasizes the distinction between self and others, and it is declared correct by modern usage guides and dictionaries. "I haven't seen any myself," "I myself haven't seen any," "Myself, I haven't seen any," and "You would even say that to me myself?" are all acceptable. But if you use them, be forewarned that someone might take exception.
In place of "me"
This one, illustrated by "There are two others here besides myself" and "He asked William and myself to do it," is generally scorned these days by those who see it as an overstuffed, self-important way of saying "me." When it is used in compounds such as "William and myself," it avoids having to think about whether to use me or I (see "'You and I' vs. 'You and me'") — but that avoidance just draws further ire from the "Don't you know grammar?" set.
In place of "I"
Using myself in place of I — exemplified by "Myself, as director here, will cut the ribbon" — is currently considered an even greater sin than using it in place of me. If myself is supposed to be a reflexive object, using it as neither reflexive nor object is guaranteed to discombobulate tidy grammar gardens. And indeed you don't so often see myself as the bare subject of a sentence, even in overstuffed business-speak. However, Shakespeare seemed to have no qualms about using it in the mouths of formal characters.
When the subject is a compound subject, myself is a bit more commonly used: "William and myself will be there" and "Myself and William will be there" are both types seen often enough. Why? It adds weight, certainly, but again, it also avoids having to commit to me or I in a compound — convenient for the speaker but irritating for the grammar stickler.
As a reflexive
This is the one that everyone is OK with: To signify that the person doing and the person done to are the same. Reflexives can be very useful for avoiding ambiguity…in third-person constructions. "They did it to them" does not mean the same thing as "They did it to themselves." In first-person constructions, it doesn't make the same difference: "I did it to me" is just an odd way to say "I did it to myself." But we use reflexives because we use reflexives, and there is definitely nothing wrong with saying "I asked myself what I could do."
There are a couple up there I haven't mentioned yet. The first one is "He was a man as big as myself." If you replace myself with me, you will have someone telling you it should be I, but if you use I, it will sound stilted to most people. Beyond that, it could just be another case of myself meaning "my self."
The other one is "I directed all inquiries to myself." Since you are doing the directing, it would seem fine as a reflexive, but since the inquiries are coming from others, it would not seem fine as a reflexive. So is it OK or not? Well, if you wish to go with 1,500 years of established usage, plus the fact that even now the reflexive is not the only correct form, you can rest easy with that one…unless your readers are particularly captious.