They're pretty much required in reflexive constructions ("He hit
himself") and some emphatic constructions ("I don't care for black jellybeans myself"). I'm guessing you're talking about other constructions, like "Please return it to either Bob or myself" or "Either Bob or myself can help you."
Merriam-Webster's Dictionary of English Usage has a great entry on those, so I'll just
link to it. Though if you have any further questions, I'd be happy to answer them.
The basic gist of the article is that it's not ungrammatical, though a lot of people consider it a stylistic sin. If you use it—especially if you overuse it—some people will likely frown on it, but that doesn't mean you always need to avoid it. My personal opinion on it: I think it sounds a little awkward at best and stilted at worst. I don't use it myself.