Which is more correct:
Recently I was hungry
Recently I have been hungry
I think that the second variant is more correct. Could you please explain to me what do you think about it. Thank you in advance.
Which you should use is entirely dependent on context. You would use the first if you are concerned to relate your recent hunger to events which occurred at that time:
You would use the second if you are concerned to relate your recent hunger to a present consequence, or if your recent hunger is a repeated state which continues to occur in the present.
There is a great deal more about this here.
It isn't that one or the other is more correct, it's that they have slightly different meanings. "Recently I was hungry" simply means that at some unspecified point in time in the past, I was hungry. "Recently I have been hungry" means that the state of hunger has persisted (either intermittently or constantly) over a period of time up till now.
This might clarify a bit:
This means that on one afternoon in the recent past I was hungry.
This means that in the recent past I have been hungry in the afternoons.
The latter sentence is something you would be more likely to hear, simply because it is something that someone would be more likely to communicate. It's talking about a recent change in condition, whereas the first sentence, if it were something to comment about, would probably include more specific information: "I was hungry yesterday afternoon."
My upvote to StoneyB and the answer is quite clear. However, I'll try to further simplify it in other words.
In general use of have been and was, the have been implies to a regular thing happening whereas was reflects the state that happened once.
Check out StoneyB's examples. I was hungry and I went to Burger King - the story is finish! On the other hand, I have been hungry took every afternoon showing some sort of regularity.
The difference of I was doing something and I have been doing something may make it clearer.