Loopwheel

Wheel with integral suspension.
Core 77
Kickstarter

Spacelander fiber-glass bicycle

Fiber-glass bike designed by Benjamin Bowdon and now for sale at Wright Auctions. "The original model included an electric motor that gathered energy on downhill and flat terrain and helped the rider climb hills." (NYT)
Benjamin Bowdon
Aqua-Velvet
Wright

Dial M for Madness

M55 Terminius Biceps electric bicycle
M55

Caminade Caminargent

1950's Caminade Caminargent bike.
eBay

Dursley Pedersen Bike

 

I have a strong memory of seeing a Pedersen bike in Christiania (Copenhagen) when I was just a child. This is a unrestored Dursley Pedersen from 1907. Lovely.
Flickr
Pedersen Bike

Les Moteurs Auxiliaires

Le Cycliste 1948

Bridgestone Young Way Monte Carlo

Pop-up headlights. So cool.
1979 Bridgestone Young Way Monte Carlo.

Thonet

Thonet bike by Andy Martin. Made using the same method of bending solid wood that Thonet developed in the 19th century and used to produce their innovative no.14 chair from 1859.
Andy Martin
Thonet
Thonet No.14 chair
Designboom

BMX Fireworks

Vis Viva

Build a rocket boys!

Builder unknown, photo taken in 1960.
Oslobilder

1980 Breezer Series I

One of the first mountain bikes, designed by Joe Breeze.

Joe Breeze

Mombat

The Chukudu

Abby Ross
Washington Post
Creative Roots

MX

1975 Moto Gori bicycle
Moto Gori

Le Tour

'Tour' chair by Rui Alves
Rui Alves

Lotus 108

The Mike Burrows designed Lotus 108 time trial bike made famous by Chris Boardman.
Lotus 108
Design Museum
Bicycle Design