Could it be some Delosperma? Only that would be an outdoor plant. Could explain the leggy stems though.

Bye, Lin

Does look like my hardy 'ice plant', agree.

It does resemble delosperma a bit, but the green bits on my mystery plant are rounded at the tips and can easily bend without breaking. It has always been kept outdoors and just brought in about a day ago--the woody, hairy stems have always been there. Here is a close-up pic. Thanks everyone for taking a look.

Consider this hairy-stemmed succulent, Mesembryanthemum hispida -- if not as an ID for your plant, then as a relative. It has the cylindrical leaves and tan, hairy stems.
http://luirig.altervista.org/pics/index4.php?search=Mesembryanthemum+hispidum&page=1

There seem to be a bunch of synonyms, including Drosanthemum hispidum, Drosanthemum floribundum, Mesembryanthemum floribundum, Rosea ice plant, Desert ice plant, and I don't remember what-all.

http://www.desert-tropicals.com/Plants/Aizoaceae/Drosanthemum_hispidum.html

The description is a bit different here, but "cylindrical, slightly curved leaves" are mentioned. Unfortunately there isn't a close-up photo.
http://mattslandscape.com/detail/?plant_name=Drosanthemum floribundum rosea iceplant

Another page:
http://www.deeproot.co.uk/pbo/plantdetail.php?plantname=Drosanthemum+hispidum

Does your plant flower? You didn't mention flowers. If no flowers, perhaps it's not happy. A bit more water, some fertilizer? Will that change the length of the stem nodes, the width of the leaves?

Or perhaps your plant is a very old variety -- maybe an original, wild species -- passed down from neighbor to neighbor to relative for who knows how long -- and what we find online are garden varieties which have been bred for lusher foliage.

This post was edited by missingtheobvious on Wed, Dec 18, 13 at 14:51

Thanks, missing! I think it may be that or definitely related. I've never seen it flower when I've grown it before or the few times I've come across it. When I fertilize and water, the leaves get a little bigger. The leaves plump up like crazy (chopstick diameter and 2 inches long max) when I foliar feed.

Really appreciate the help. I may buy the plant so that I can compare.
Cheers!