Guess the 'contorted/corkscrew' selections, like Morus 'Unryu'/Tortuosa, Corylus 'Harry Lauder's Walking Stick', corkscrew willow, etc., come to mind, first off.
I have a local eastern black walnut selection with serpentine growth habit reminiscent of, but not quite so pronounced as the corkscrew willow/hazel/filbert.

Cutleaf/fernleaf elderberry & black walnut('Laciniata) are interesting, as well.

Not sure if it qualifies as bizarre or not but this one is quite a character.
Poncirus trifoliata 'Flying Dragon' is tough and adaptable. One note, clean up the fruit, otherwise there will be hundreds of seedlings.
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Not a tree, but I'd have to say Corokia cotoneaster, aka wire netting bush, which tends to look more dead than alive for a good part of the year.

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There ARE leaves, but tiny and not too plentiful :-)

Fagus sylvatica 'Purpurea Tricolor' (shown) is quite the attention getter. It crisps up in the fall down here but nothing is like it in the spring.

There is a chocolate mimosa that is odd odd odd.

Metasequoia Ogon is another. I look at one everytime I go outside so I forget how unusual it must be for the common person. I hope the next yellow metasequoia cultivar gets the trunk of the species.

Rhus typhina tiger eyes is an unusual plant also. One of the few I have successfully grown and then "unplanted". Where it was I just couldn't deal with the suckers.

Populus deltoides 'Purple Tower' - as purple as any tree I've seen. Even young bark is purple.

pics of purple tower look spectacular, though oddly enough all the pics seem to be foreign, you see anybody offer it over here?

There is a wholesale nursery in OH that sells P. deltoides 'Fuego' - not sure how it compares to 'Purple Tower".

There exists a love/hate relationship with variegated foliage. Here's Cornus alternifolia 'Argentea' taken Sept 1. The white tends to become pinkish as we get closer to frost.
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Pin Cushion Honeylocust is termed "bizarre" in the link below. But it's not quite "commercially extinct" - there are still a couple growers producing it, including Forestfarm.

Here is a link that might be useful: Pin Cushion locust