Most knitters who've moved beyond the very basics probably have grasped the general point of why you'd want to use both right-leaning and left-leaning decreases, which is so that you get a similar appearance on both sides of a symmetrical piece of knitting. However, many knitters are much less sure about which direction of lean you want where, and what difference it makes, so let's take a look at that.
When using paired decreases, there are basically two choices available to you. You can use decreases which lean into the center of the piece, or decreases which lean away from it.
When you use, for instance, a right-leaning decrease, the appearance of the two stitches decreased is that the leftmost stitch is on top, leaning toward the right, and the rightmost stitch is neatly tucked up beneath it. If you place this right-leaning decrease on the left edge of a piece of fabric, and do a series of decreases which are each an equal distance from the edge (such as, for instance, knitting until 3 stitches remain, and then doing k2tog, k1), you will get a very clear line coming up the left edge of the fabric, as each of the leftmost decreased stitches lines up on a diagonal. The same is true, of course, of a left-leaning decrease placed on the right edge of a piece of fabric. This type of decrease placement, where decreases lean toward the portion of the fabric which is getting smaller (usually, but not always, the center), is called a "strong" decrease. It's commonly seen on places like sock toes and gussets, where the strong line produced is a part of the design.
When you use, instead, a left-leaning decrease on the left edge, the decreased stitches don't align visually. With this type of decrease, the rightmost stitch is on top, and lies at an angle to the line of the fabric edge, so there's no continuous feature. Again, the same is naturally true of a right-leaning decrease on a right edge. This type of decrease placement, where the decreases lean away from the portion of the fabric that's getting smaller, is called a "feathered" decrease. It's commonly seen on armholes and sleeve caps, especially on commercial knitwear, and can be used anywhere that the strong diagonal line isn't desired. It's still visible -- there really aren't any invisible decreases, in contrast to increases -- but it's much softer.
[Edit: It occurs to me that I have a bit more to add here, about why the strong and feathered decreases form. When decreasing, one column of stitches appears to survive, and one to tuck beneath it and disappear. Strong decreases form because the decreases are placed so that the same column is always the "survivor"; with feathered decreases, in contrast, the column that disappears in one decrease is the one that was the "survivor" from the prior decrease. In the example above, where "k2tog, k1" is done at the left edge of the fabric, the second column from the edge is always the "survivor" from the k2tog decrease, and thus forms a strong decrease; if "SSK, k1" were done at the same location, the 3rd stitch from the edge would be the survivor, and would become the 2nd stitch from the edge, to be eaten up in the following decrease.]
As for which right-leaning or which left-leaning decrease to use, that's up to you. As discussed when we were talking about the single knit decreases, SKP and SSK are structurally the same, and so are k2tog and KRPR; the difference, if any, comes from your execution, so use whichever you're the happiest with.
What about the centered double decreases? Again, it's a matter of whether you want the strong line. The S2KP produces a very prominent line of single stitches, which appear elevated from the surface of the fabric. Sometimes this is a great design feature and can be used as an accent. If that's not desirable, then the softer, more feathered, SK2P should be used.
I hope you've found this interesting; if so, you may want to take a look at Eunny Jang's wonderful piece on the structure of lace, part of her incredible Majoring In Lace series. She shows a number of the beautiful effects that can be achieved by the way decreases are aligned, and it's fascinating.