Why are they there? What function do they serve, other than to help identification?
Did God say to Himself, “I’ve got a bad feeling about some of these guys. Think I’ll put in a little extra to help law enforcement.”
This may be an answer but as is often the case - no one really knows.
I’ve seen them all, and man, they’re all the same.
-Paul Simon
Research hypothesizes they may improve grip on rough surfaces, provide greater ability to stretch and deform, improve touch sensitivity, allow water drainage to improve grip on wet surfaces like tire treads, or likely all of the above in some capacity.
If you read that article you may have problems with its tone and their conclusions, like I did. Of course the ridges do not improve grip on perfectly smooth surfaces; where the fuck is a primate going to encounter a perfectly smooth surface in nature?!
The above-mentioned article is summed up (no doubt by a journalist, not a scientist) as “Scientists have proved that instead of improving your grip, fingerprints drastically reduce friction.” It goes on to describe convoluted experiments using fingers with normal fingerprints in a lab (read artificial) environment. No mention is made of any testing done using fingers that don’t have fingerprints.
People who don’t have fingerprints will tell you that they certainly do help with grip on smooth objects in real life. These folks have to be extra careful how they hold things – a drinking glass may slide out of their hand. This article mentions the poor grip, saying “…the lack of fingerprints deprives her of some grip, which makes dealing cards or turning pages more difficult.” I’ve seen other references in print but I don’t recall where and they’re hard to find because googling turns up a jillion references to the study mentioned above – the study that studied fingerprints rather than the lack of fingerprints.
So, despite the highly touted and way-too-oft-repeated claims based on a flawed study, fingerprints do serve to help with gripping.
None of which answers the question of why fingerprints vary so much in pattern, so much so that they are effectively unique to every human ever born. Why not some regular pattern, or some simple set of patterns? (Yes, I know there are only a few basic patterns, but the genetic persistence of certain patterns and myriad sub-patterns seems so… complicated, to no evolutionary end.)
Between his or her legs, or those of his mate? - only slightly joking, here.
Pretty much everything about us is unique–DNA, lip prints, retinal blood vessel patterns, etc., etc. Fingerprints are just easy to record from a person and detect when left on surfaces, so it was adopted early for ID. There is very little about us that is based on a common regular pattern.
Well, there’s that bilateral symmetry thing, you know. 
I guess the answer lies in something like fractal algorithms regulating the distribution of the body’s micro-elements - that is, there’s no specific genetic control of how retinal vessels are routed, just an algorithm that spreads them out in an effective pattern, unique to the vagaries of the individual’s DNA and development.
Fingerprints just seem… weird on this scale. (And do fall into four or five basic patterns, as well - loop, whorl, etc.)
They most certainly help. As a professional cook, I have discovered that there are some tasks - like peeling potatoes - that are next to impossible if you try to do them while wearing those latex gloves. Damn potatoes keep sliding out of your hand and into the trash. So, barehanded it is. (Which is okay, because the potatoes will be cooked afterward.)
WAG: The existence of fingerprints is under genetic control and, overall, their form, but the details are caused by random fluctuations in the womb. I remember reading something about the Dionne quints, that three of them were mirror images of the other two, as seen from their fingerprints. meaning that some twinning had occured after chirality was established. But even so, they were not identical.
IIRC, the same applies to ear shape. A person’s details of the ear convolutions are fairly specific to them.
Smooth surfaces? A lot of fruits and berries tend to have relatively smooth skins. Debarked wood can be pretty smooth. Sea shell interiors. There are some fairly smooth surfaces encountered in the wild…
I believe that it’s just random, like how a snowflake can develop into an infinite number of different patterns, based on some simple chaotic factors. There’s some simple rule, in our DNA, which says “Thou shalt have fingerprints!” And then, during the construction phase, the builder cells just sort of figure out something that follows the general rules. There’s nothing preventing duplicate fingerprints from occurring. It’s just highly unlikely that the same result will be generated twice.
So it does come back to the hypothesis in my OP!
A security measure to confirm identity of arrivals at the Pearly Gates.
Another poster hinted at this, but besides genetics their pattern is determined by the unique way you move in the womb, at least according to my pregnancy book.
Lots of natural patterns can be formed by a set of simple rules that depend only on neighboring cells.
Imagine for the moment that you have cells on a rectangular grid. Each cell can turn black or white, and has this rule: add one point for each of the closest horizontal neighbors that are black, and for each vertical neighbor that’s white. If the answer is 3 or 4, then turn black. If it’s 0 or 1, turn white. Otherwise, stay the same.
Now, we start with a random pattern and then iterate our rule. Thinking on it a bit, we can see that the most stable pattern is alternating horizontal stripes. But it doesn’t say if the odd or even stripes should be black, and furthermore there’s no guarantee that distant cells will agree on this. Most likely, it will converge on a picture where small regions show the stripe pattern, but with randomness to how the regions are arranged.
Now, clearly this is a simple and artificial example, but it’s likely that fingerprint formation follows a similar kind of approach. You start with some sheer randomness. Then, as new cells are created, they follow some kind of local rule–something along the lines of “if it looks like I’m part of a ridge, emit some signal that spurs the growth of more cells.” A set of random initial bumps will then progressively get more ridge-like, but in a random way that’s unique to the individual.
It’s thought that some animal patterns, like tiger stripes, work in essentially the same fashion.
You need them to judge the sharpness of a knife.