As in このオレさま and この僕も. I know the literal translation, but I never understood what the intent of it is.
I think この usually implies some quality of “me”. You can translate it as “someone like me”. You can insert some adjectives between この and <first person pronoun>.
Usually it sounds proud or arrogant, especially in このオレさま.
But as Hyperworm pointed out, it can be used in exactly the opposite sense. e.g.
I think この私 tends to refer to some positive quality, and こんな私 some negative quality. But I'm not sure.
「よく聞け！私はお前達とは違うのじゃ！だからして…この私に気安く話しかけるでないぞ！分かったか？一般人ども！」 ｂｙ 久地院美華
I think this is a pose of この私. (Does anyone know the name of this pose?)
"The guy standing here in front of you"
"This guy here"
"The guy you're looking at"
Some clarification as noted by the commenters. Yes, オレ and 僕 or course refer to the speaker. So the question is, what is the nuance introduced by the demonstrative adjective この? It is "this me", as opposed to some other "me", such as a "me" at some other point in time, or a hypothetical "me" in some other situation. Since "this me" is ungrammatical in English, we need some other word to stand in for "me", for which I chose "guy", although I suppose there are equally good alternatives. Another way of introducing this nuance would be with a formulation such as "right now I..." or "standing here I...".
The words kono, sono, and ano, (interrogative dono) are deictic demonstratives. Their deictic meanings operate along a proximal-distal dimension.
kono = proximal to the speaker
sono = proximal to the addressee
ano = distal to both speaker and addressee.
This kind of deictic meaning is not restricted to kono, sono, and ano. There are at least these additional forms:
adnominals: kono, konna [emphatic]
nominals: kore; koko
adverbs: koo, konnani [emphatic]; kotira, kotti [emphatic]
This type of deixis is expressed by the entire paradigm, and not only by kono, sono, and ano.
Speakers are always proximal to themselves. Hence, one must use kono with a pronominal expression referring to the 1st person.
However, kono itself does not express meaning in the modesty-respect dimension. This dimension is referenced by the pronominal expression: 俺 is far less modest than 私, and that leads to the differing nuances of この俺 and この私.