Speaking without any references:
I’m under the impression that a lot of surnames arose from personal situations associated with people.
So you have occupations (Smith, Miller), colors, (Brown, Green), locations (Rivers, Fields), and so forth.
But what is a “Jones?” It’s a common name without an obvious (to me) origin.
Maybe it’s Spanish in origin, and it’s short for “cajones.”
OK, just kidding. Failing a satisfactory answer, my WAG is that it’s somehow a variant of John/Johns/Johnson.
The final S indicates a probability of Welsh origins (think Davis, Ffolkes, Evans, etc.) (This only works for names that sound vaguely British; Santos is not Welsh.)
What’s In a Name, by Rule and Hammond, backs this up, claiming that it is Welsh from Latin Johannes–John.
Tom~
Mjollnir:
I’m trying to visualize those “personal situations” not “associated with people.”
So maybe ‘jones’ came from ‘Jonah’s son’.
tomndebb:
But the sound of one “British” clapping doesn’t sound like the next British clapping, if “British” = English / Scotch English or Welsh – or does “Welsh origins” = origins in English names used in Wales? In the cases you speak of, does the ‘s’ to the genitive, to ‘son’ or what?
Ray
Maybe the name comes from their tendency to long or desire to do stuff. The original Jones may have got those travelin’ jones, or those “need to post a dumb joke disguised as a WAG” jones, or…
…Sorry, I guess it’s just in my jones… 
Cornflakes can be a jones, as can bastitbaw.
On this page:
http://www.library.ubc.ca/jones/vanety.html
It says:
“Any Western surname is likely to reflect one of four things: an occupation (Smith), a parent’s given name (Jones – son of John), a place (Field), or a personal characteristic (Brown).”
Ray (an occupational type presently w/o an legitimate occupation, which explains why you’re reading this)
And this page:
http://www.nii.net/~yonts/Section%2001a%20-%20Yonts%20Etymology.htm
says ‘Jones’ is a Welsh version of ‘Johnson’. And you can dance before that door to knowledge forever, because the author, lost in his constipated etymology, never gets off the John.
Ray (They musta always had daughters; never yet’ve heard of a Raymondson.)
And this page:
http://www.qsl.net/g7exo/evans.htm
says ‘Jones’ = ‘Evans’, which are both Welsh, and they equal ‘Johnson’ in English.
Ray ('Evans, would I Welsh on your bet?)
That’s because over time, the name came to be spelled Raisin. A lot of them settled in California. Or at least that’s what I heard through the grapevine. 
Okay, but how did the phrase “jonesing,” as in “Man, I smoked a bowl, and I’m jonesing for some munchies right about now” develop?
Yer pal,
Satan