There are several hundred species of Aristolochia, broadly consisting
of evergreen or deciduous, tropical, sub-tropical and warm/cool
temperate, vines plus herbaceous perennials that die back to thickened
rhizomes and/or tuberous roots in winter. Many of the herbaceous
perennials are very hardy, but of little horticultural interest with
small, relatively dull, albeit fascinatingly constructed flowers that
are often hidden by the foliage. Some have attractively veined
leaves, but few have 'wow' factor.

The hardy vining species of which there are about a dozen that could
be described as truly hardy have rather unimpressive flowers.
Considering the amount of growth that they make, the reward for the
space taken is not enough to warrant their inclusion in many gardens.
Only a few are widely available and personally. I'm not convinced they
are worth making concerted efforts to track them all down. Unless
you're a botanist that is.

Aristolochia durior (macrophylla) was quite often offered as a garden
climber in the 1960's and 70's, but seems to have all but disappeared
from the garden centres after that. It is a vigorous, utterly hardy
climber with masses of large, heart shaped leaves that hide the rather
small creamy green, marked brownish red flowers in late spring. It
easily clambers to 10m. and was often used for pergolas. The foliage
is nice, but not nice enough for my liking nowadays. I had it running
over a dead tree, but later sent Rosa filipes 'Kiftsgate' up for a
'scrap'. The rose was infinitely more rewarding with its countless
thousands of scented white flowers and the Aristolochia was
subsequently chopped to the ground. It never quite recovered -
possibly because any new shoots that re-appeared were yanked out
during weeding exercises..

A. tormentosa is a pleasant, fairly vigorous vine with leaves that are
finely hairy, felted even and small, quaint green flowers with a brown
smudge at the entrance to the tube. It is hardy and looks reasonably
impressive especially in light shade where the leaves can grow to a
fair size. I grew it at Bromsgrove, but would not do so here - or
recommend it with great enthusiasm to any one else for that matter.
Each to his own, but in my view there are climbers with better
foliage.

The really glamorous 'show-stoppers' tend to be decidedly tropical in
their origins and most need considerably humidity and warmth to do
well. Some have very broadly flaring lips to their tubes and are
often known as 'Calico flowers'. Others have very intricately
constructed pitcher-like flowers reminiscent of the leaf traps of
Nepenthes and like them, mostly demand very high heat and humidity. A
couple of the 'Calico flowers' have limited potential for very
sheltered, near frost free gardens in the far west and south of the
UK, but are definitely not suited to growing out of doors elsewhere.

Aristolochia littoralis can cope with southern UK winters if the roots
are well mulched and the new shoots protected from slugs and snails.
In a good year it will clamber to 2 metres or more and produce a
succession of rather showy, 6cm. wide, creamy white, flared 'pipes'
that are veined and mottled maroon. I grew it in a cold greenhouse at
Bromsgrove and am thinking about planting it here.

A. gigantea has already been mentioned and it is somewhat more
tender. It performs best if the stems are not cut back by winter cold
and therefore needs a very sheltered site. However, it can rejuvenate
quite well from the roots, but it needs an early, very warm start to
spring and a long hot summer to make up. Get it right and the lavish,
heavily shaded deep red flowers up to 12cms. across are worth the
effort. It is on my list for here since I've got an almost perfect
spot currently being abused by an excessive Jasminum polyanthum.

A. pearcei is a relative newcomer to the gardening scene and one which
I'm in the process of trying out. There are forms with deep green to
almost yellow, 8cms. long, 'tuba-like' flowers and foliage that is
faintly or heavily marked with silver. Really good ones have heavily
silvered veins and almost yellow flowers. Being a native of southern
Chile, pearcei is hardier than the above species, but still needs a
warm sheltered site to do well. Given support it can scramble up to 2m
or more although it appears equally at home sprawling across the
ground.

So, back to the original OP and his question, yes there are more
species than you could shake a stick at, but if you want the lavish
and extravagant 'calico-flower' types, they will not survive in a
Midlands garden even with the warmer climate of recent years. Some of
the hardy climbers have merits as large leaved foliage plants, but the
flowers leave a lot to be desired if you want glamour and pzazz.