The real wacky races: The weirdest ideas for a new way to get to work

A few days before the city was saturated by the force of Superstorm Sandy, New Yorkers took to the city's High Line walkway in autumnal shirt sleeves. Tourists shuffled along while querulous New Yorkers grumbled over their flat whites-to-go. The High Line has had two innovative incarnations: first as a raised railway which threaded through warehouses from 1934 to 1980, then latterly as a tree-lined pedestrian path above the choking traffic.

The High Line's success has inspired a new generation of dreamers bent on transforming the way we travel around our cities. "We love the High Line, it's our main inspiration," agrees Y/N Studio's Alex Smith, who came up with the recent Lido Line proposal to allow commuters to swim to work along the Regent's Canal. "Our idea offers Londoners a new way to traverse the city."

Across the Channel meanwhile, you couldn't imagine a more French way to cross the Seine than by bouncing over it on trampolines. Sartre would have loved Atelier Zündel Cristea's joyously barmy scheme for a Parisian bridge you bounce across.

The Trampoline Bridge and the Lido Line aren't quite as close to April Fool's Day territory as they seem. We never got the hoverboards we were promised in the movies. But ideas such as railways running under our feet or trains flying on magnets were similarly scoffed at. Yet London had the first Underground by 1863 and Birmingham ran the first Maglev in 1984.

In the 1800s railways were the future, in the 1900s roads were. Both contributed to centrifugality – the rich moved to suburbia, draining city centres. This century's innovators are concentrating on greener projects which reconnect us with the city. Boris Bikes and cycle superhighways encourage new cyclists. But what about cycle lanes in the sky? "SkyCycle is akin to a High Line experience, providing cyclists with a direct route into central London," explains Sam Martin of Exterior Architecture. Developed with Foster + Partners, Martin's concept envisages bike lanes on railway arches, because "the bicycle will, in time, become the dominant mode of transport". Cycling in the UK has increased by 12 per cent in the past decade – in London by 110 per cent. Twentieth-century car culture was masculine and atavistic, but the explosion in city cycling is increasingly female: fuelled by girls astride Dutch bikes, for whom two-wheeled transport (plus basket) is a statement of intent.

Fashions affect the transport systems our cities get. But money plays a greater role. The Metropolitan Railway's Home Counties "Metroland" extension let it play property developer in the 1920s. In the 1940s, General Motors, Standard Oil, Firestone Tyres and Mack Trucks conspired to break up tramlines from Cleveland to Los Angeles. The Great American Streetcar Swindle sowed the seeds for America's auto addiction. In 1960s Britain, miles of urban motorways were signed off by transport minister Ernest Marples – whose company Marples Ridgway also built those roads.

Now tech firms are in the ascendency and their cash is driving policy. Google is developing a car which controls itself , a Prius loaded with lasers, cameras, radar and – yes – Google Maps. Following intense Google pressure, California changed its laws in September so the self-driving car could be tested on San Francisco roads.

The internet behemoth has thrown its weight around elsewhere: pumping £600,000 into New Zealand's Shweeb. Named for the charmingly anachronistic Schwebebahn (hanging railway) in Wuppertal, the Shweeb slings a recumbent bike beneath a monorail track. "The 20th century was just a brief excursion into what transport might look like with unlimited cheap fuel," quips Shweeb inventor Geoffrey Barnett. On the Shweeb in Rotorua, you can pedal at 40mph.

But Volvo reckons commuters won't give up their cars. Its plan involves road trains – car convoys follow a lorry and "drive" themselves. "We extended the camera, radar and laser technology used in safety systems," explains Erik Coelingh from the Swedish manufacturer.

Lobbying by powerful technology, construction or manufacturing corporations can't be underestimated. "There's no lobby for Maglev, a lot for rail," sighs Reiner Köhler of Munich's Transrapid. Its 20 mile-long test track – where magnet-powered trains ran at dizzying speed – closed last year. "It costs €5m a year to keep it running and demand isn't there." Maglev was one of the great hopes – Shanghai installed the world's fastest in 2001. But the technology flopped. Köhler laments: "The rail transport market isn't innovation driven."

But there is small-scale rail innovation. The Parry People Mover is a modest railcar using a car-sized engine and a flywheel to harness braking energy. A PPM prototype runs on the Stourbridge Town branch line. "There's interest from Britain, Australia, Spain, Turkey, the US, and Latin America," boasts inventor John Parry. It's cheap too. Bringing back trams was the thing in the 1990s – but infrastructure costs. Edinburgh's trams are wildly over budget; Leeds, Liverpool and London put tram plans on ice. Cambridge went for a busway – a concrete track for buses. York tried the widely-ridiculed 'ftr' – purple bendy buses disguised as trams. They were unceremoniously scrapped in March.

Developing cities cry out for mass transport: in Sao Paulo traffic is so bad that the wealthy dart between skyscrapers in helicopters. In the Punjab capital Amritsar, Ultra is building its futuristic Personal Rapid Transport system – automated pods which glide on a track above choked streets. But are expensive projects what poor cities really need? Prototype pods operate at Heathrow, while Ultra's home city of Bristol is mulling a PRT system between Cabot Circus and Temple Meads.

Back at the High Line, the tracks stretch into the distance – an extension will swoop over the Hudson Rail Yards in 2014. Who knows what the future city will look like? But with all these new transport ideas on the table, one thing's for sure: eventually, where we're going, we won't need roads.