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The tropical Asian genus Trichotosia has species with hairy stems and a growth habit of this kind.
I responded to this a couple of days ago, suggesting P. mirabilis as a likely identification.
A very well fertilized Peperomia, but not sure of the species name.
It's a Plectranthus without doubt, I would have thought Plectranthus neochilus, which is often erroneously identified as "Cuban oregano".
Why isn't it a hollyhock (Alcea rosea)?
Looks like Ulmus parvifolia.
Maybe Tecoma castanifolia, which is native to Ecuador. See TROPICOS database at http://mobot.mobot.org/cgi-bin/search_vast Search on this...
Dianella certainly, but not D. caerulea, which is our common east-coast species here, in moister habitats especially. Dianellas are difficult to...
I suspect Capparis cynophallophora.
This is Semecarpus cochinchinensis, family Anacardiaceae. The sap is highly irritant to the skin.
Michael, is it really your opinion that North Americans need to be "educated" to your system of "standard" British common names? It seems...
It's a Chaenomeles, or flowering quince. The rounded "leaves" close to the stem are stipules, which are appendages of the leaf stalks commonly...
These look like Turnera subulata and Butea monosperma.
I did suspect C. verrucosa as a possibility, but only a possibility as there are other spp. with warty cone-scales like that. Liz, Callitris is...
Could be Asparagus asparagoides.
Callitris, but I can't say which species. The cone-scales in whorls of 3 are diagnostic.
The name Tradescantia fluminensis is used rather loosely, or at least it is a variable species with several distinct races. One of these (often...
If it's a "vine" of over 15 ft as you say, there are 2 likely candidates among commonly grown cacti. First is Selenicereus grandiflorus with...
Not Port Jackson Fig (F. rubiginosa), which is a local native for me and I see it at all sizes. I agree with Saltcedar, it's F. microcarpa.
Right one more like a Lampranthus -- a large genus, identification of some of the cultivated species very difficult.