Many black & white edits one can see nowadays contain these really striking, dramatic and dark skies. It is often attributed to the combination of a red filter with a polarizer, but from my tests with a red filter I can assure you that it is not possible to get that effect straight out of the camera - at least not with digital (depending on the time of day, the red filter will have surprisingly little impact to the brightness of the sky). Maybe things are different with film - I don't know.
Anyhow, it's not all too difficult to achieve a similar effect in post processing, and it's not really necessary to use specialized black & white conversion filters/plugins for it - Lightroom alone does the trick pretty well.
I've explained how to achieve an infrared look in post processing with Lightroom before and the technique I described there to get really deep and dark blue tones can be further enhanced with local adjustments. That can be the local adjustment brush, or a graduated filter, like in my example below.
Here's the - otherwise finished - image with a "normal" sky (click to enlarge):
And for your comparison, here's the "more drama" version with a graduated filter to darken the sky (again, click to enlarge):
The "trick" is to combine a decreased Brightness/Exposure* with increased contrast on the local adjustment/graduated filter. More contrast means: dark tones become darker, and bright tones become brighter - by compensating the increase of brightness in the highlights (due to contrast being at +100) with a decrease of Brightness/Exposure, we can get a darker sky while the clouds appear almost unaltered.
Needless to say - the source material is important, just as always. This was late in the afternoon and the sky was not too brightly blue anymore and I used a polarizer to further darken it (I couldn't use full polarization though - at 16mm wide angle on full frame, it would lead to a very uneven darkening of the sky).
*) Lightroom's Brightness control is a midtone adjustment that has less effect on the highlights and thus is my choice for this type of edits, or brightness adjustments in general. If you need to brighten an image without blowing out the highlights, leave the Exposure setting alone and adjust Brightness instead - it's nicely illustrated in this video on YouTube.