Motorcycles are a kind of love-or-hate thing, usually bashed for the absence of comfort features or weather protection for the user, and lack of cargo space, making them unpractical to haul bigger objects. Their low fuel consumption can become appealing for people who hate Diesel-fueled cars, alongside the hybrids. But, considering the environmental aspect, the motorcycles make way more sense than a hybrid econobox, i.e. a Toyota Prius.
One of the main arguments towards hybrids, apart from the "motorcycle-like" lower fuel consumption comparing to an average non-hybrid econobox, was related to the permission to use it in HOV lanes even when the driver was
forever alone. This benefit, which led to a massive amount of hybrids in places like Los Angeles, came to an end recently, since they don't qualify for alternative-fueled vehicle incentives anymore, altough it's still valid for motorcycles. Considering the lesser space taken at the road surface by a motorcycle proportionally to the passengers capacity, they also make more sense in matter of traffic jam reductions.
No matter if it's a tiny Lambretta or a big Harley-Davidson, the size-to-occupation density is higher, so less space is taken at the road surface for each person transported by them instead of a Prius.
Even an old-school motorcycle with a simple carburettor-fed engine can still get better mileage than a hybrid car, altough nowadays the electronic fuel injection becomes prevalent.
Another aspect to consider is the amount of raw materials involved in the manufacturing of the whole vehicle, replacement parts (i.e. tyres, lamps, spark plugs, coils and cables, shock absorbers, friction material for clutch and brakes, among others) and other products needed to keep the vehicle operating properly, such as lube oils and greases, no matter if the car is a subcompact such as the Chevrolet Spark or if the fuel consumption is not so much more advantageous for the motorcycle, it's still usually more efficient from the factory to the end-of-life disposal.
A specific application where motorcycles can show other advantages is recreational off-roading: dirt-bikes are usually even more compact and lighter than a road-legal one, which increases their maneuverability in tight spaces where a Jeep would be too big to pass safely.
The lower weight also copes to reducing the risk of getting stuck in a mud pit, and is also easier to recover if gets stuck. Environmentally-wise, apart from the lesser amount of fuel and lube oils, motorcycles generate a lower pressure over the soil, in spite of the smaller contact surface due to narrower tyres. Basically, assuming that the contact with the nature is an essential part of recreational off-roading, the only disadvantage of motorcycles in this application is the lesser capacity to carry passengers, tools and replacement parts (and also a grill, charcoal, some beef and beer for a tailgate party) comparing to a 4WD.
After all, motorcycles have been a good answer to the demand for fuel-efficiency and an overall low running cost.
