When is it correct to use "yourself" and "myself" (versus "you" and "me")?

Both of these are incorrect. The reflexive pronouns (myself, ourselves, etc.) are only used when the pronoun is the object of a verb having the same subject, e.g:

I love myself. (Subject and direct object are both the speaker)

Give yourself a raise. (Subject is you, implied from imperative, indirect object is you).

The other answers stating that reflexive pronouns can only be used as the object of a verb with an identical subject are not entirely correct. Reflexive pronouns can also be used for emphasis as in “I myself will go” or in absolute constructions “myself a tourist, I nevertheless avoided other tourists”. These examples come from Merriam-Webster's entry for myself. That entry has a usage note intended to disabuse the common claim that reflexive pronouns can only be used in restricted cases:

usage Myself is often used where I or me might be expected: as subject <to wonder what myself will say — Emily Dickinson> <others and myself continued to press for the legislation>, after as, than, or like <an aversion to paying such people as myself to tutor> <was enough to make a better man than myself quail> <old-timers like myself>, and as object <now here you see myself with the diver> <for my wife and myself it was a happy time>. Such uses almost always occur when the speaker or writer is referring to himself or herself as an object of discourse rather than as a participant in discourse. The other reflexive personal pronouns are similarly but less frequently used in the same circumstances. Critics have frowned on these uses since about the turn of the century, probably unaware that they serve a definite purpose. Users themselves are as unaware as the critics—they simply follow their instincts. These uses are standard.

Merriam-Webster’s Dictionary of English Usage also has an extended discussion on the various uses of reflexive pronouns which you can read on Google Books, giving examples of myself being reasonably used in many positions other than object of a verb with an identical subject.

This is a classic example of overcorrection as a result of learning language rules at school.

Accusative pronouns have had a tough run in the past 100 years in English. In school, we were always taught to say "Sarah and I are going to the park" instead of "Sarah and me" or "Me and Sarah", and so on. But what often either fails to be conveyed (or is lost on the student) is that this only applies to nominative case; that is, it applies to the subject of the sentence only. Because subjects and objects and case markings are things that people don't normally explicitly think about when making a sentence (your brain pretty much computes this for you), they get it wrong when trying to apply the rule. So, you get people saying "Please see Sarah and I", even though it should be "Sarah and me" because it is the object of the sentence. All of this has had the effect of (in my observation) the accusative pronoun (particularly the first-person singular pronoun) being looked at as somehow informal or uneducated sounding.

Another method of avoiding the accusative pronoun that people have stumbled upon is using the reflexive pronoun, and this is what you're seeing. So, instead of saying "please schedule a meeting with John, Mary, and me" (which is 100% correct), some people perceive it as more educated/formal to say "please schedule a meeting with John, Mary, and myself".

The entries for the reflexive pronouns (‘myself’, ‘yourself’, &c.) in the OED seem to indicate that they are used when the object and subject are the same (‘I confuse myself’), or for emphatic purposes (‘I myself am lost’). However, the use of the reflexive pronoun as either a direct or indirect object (‘He gave it to myself’) seems to be acceptable in Irish English.

In the given examples, only the second forms would be proper; the first are incorrectly using reflexive pronouns are being used as indirect and direct objects.

It is very simple to remember when NOT to use the pronoun "myself." Don't use "myself" unless the pronoun "I" has previously been used in the SAME sentence. Someone needs to inform 99% of those in media of the correct usage of "myself." I cringe each time I heard or read it used incorrectly.

"Please don't hesitate to contact myself [me]."

I frequently hear this mistake in a business setting. I suspect people overthink it and use the longer word—as they've heard peers do—incorrectly. It's a misguided affectation and that's why it provokes such snobbery. The intent is to sound well-spoken, but it has the opposite effect.

Like the greengrocer's apostrophe, it seems to be seen less often in casual writing.