For the September challenge several members commented on the Am – Dm – G – E progression, saying that they liked (or didn’t like!) the fact that that E chord was “out of key”…
That statement is not correct: that E chord is indeed part of the “key”. In fact, one may argue that it is necessary for that chord to be major in order for the progression to be in the A minor key!
With the progression Am – Dm – G – C we are arguably more in modal Aeolian territory than in the A minor key!

The major mode is simple: it is supported by the major scale T 2 3 4 5 6 7 8

The minor mode is much more subtle and more complex because it has not one but three scales:
– the natural minor scale: T 2 b3 4 5 b6 b7 8
– the harmonic minor scale: T 2 b3 4 5 b6 7 8
– the melodic minor scale: T 2 b3 4 5 6 7 8

Please don’t confuse keys and scales!

For example, for the A minor key we have:
A natural minor scale: A B C D E F G A
A harmonic minor scale: A B C D E F G# A
A melodic minor scale: A B C D E F# G# A

The natural minor scale doesn’t have a leading tone, so the dominant chord is minor and the perfect cadence is v – i, which is a tonally weak cadence (but perfectly pleasant in a modal context!).
Raising the 7th degree of the natural minor scale produces the harmonic minor scale; with that scale the dominant chord is major and the perfect cadence is V – i, which is tonally desirable.
But in the harmonic minor scale there is now an augmented second interval between the 6th and the 7th degree, and that’s melodically awkward (try to sing it!). To compensate for that, raise the 6th degree by a semitone and you get the melodic minor scale.

That melodic minor scale is a bit peculiar: it is played as indicated when going up the scale, but when going down, the natural minor scale is used instead. This is because when going up, you hit the b3 that unmistakably defines it as minor, whereas when you go down you start with something that sounds like the major scale. In order to impose the minor personality the natural minor scale is used instead on the way back. (But jazz musicians don’t really care – particularly those if the be bop period!).

So, depending on which scale you use, the chord family for a minor key is:
i (ii° ii) (bIII bIII+) (iv IV) (v V) (bVI vi°) (bVII vii°)
In practice, the ii, bIII+ and vi° chords are rarely used, which leaves us with
i ii° bIII (iv IV) (v V) bVI (bVII vii°)

If we group these chords into the traditional harmonic functions we get:
Tonic function: i
Predominant function: ii°, iv, IV
Dominant function: V, vii° (and possibly v)
Unspecified (variable) function: bIII, bVI, bVII

For example, in the A minor key we have
Tonic chord: Am
Predominant chords: B°, Dm, D
Dominant chords: E, F#° (and possibly Em)
Unspecified: C, F, G

“Unspecified function” means that the corresponding chords can take up different functions depending on the context in which they operate.
So, in the progression |Am – – – |G – – – |E7 – – – |Am … etc… the G chord (bVII) functions as a predominant chord, whereas in |Am – – – |Dm – – – |G – – – |Am … etc… that same G chord functions as a kind of dominant (since it leads to the tonic chord).
Very often chords don’t have any other function than to prolong the previous harmony. For example in the progression |Am – – – |G – – – |Am – – – |Dm etc… the G chord is only there to prolong the tonic harmony; it has no other function.

In minor keys, it is extremely frequent to mix the various chords. So the very common major I – IV – V – I progression has the following possible translations in minor:
i – iv – v – i
i – iv – V – i
i – IV – v – i
i – IV – V – i
Let your ear decide what you prefer!

Here is the chord progression for “House Of The Rising Sun”:
|Am – – |C – – |D – – |F – – |
|Am – – |C – – |E7 – – | – – – |
|Am – – |C – – |D – – |F – – |
|Am – – |E7 – – |Am – – |E7 – – |
It’s definitely A melodic minor since we have a D chord.
That D chord harmonizes a D note in the melody, so you could technically replace it with a Dm – some do it for that old time feel. But I personally think it has much less “juice”.
Also, if you play
|Am – – |C/G – – |D/F# – – |F – – |
you get a nice descending bass line that you don’t get with a Dm chord.
Similarly, you could replace E7 by Em(7), but somehow that doesn’t seem to cut it…

Conclusion
In any minor key, the V chord is perfectly legit. It is NOT a borrowed chord but an intrinsic part of the key.