Electric bicycle fits under the definition of "moped" under Kentucky law. You don't need tag or insurance, but you need a driver's license. "Moped" means either a motorized bicycle whose frame design may include one (1) or more horizontal crossbars supporting a fuel tank so long as it also has pedals, or a motorized bicycle with a step-through type frame which may or may not have pedals rated no more than two (2) brake horsepower, a cylinder capacity not exceeding fifty (50) cubic centimeters, an automatic transmission not requiring clutching or shifting by the operator after the drive system is engaged, and capable of a maximum speed of not more than thirty (30) miles per hour[94][95] Helmets are required.
I would advocate you ride legal within the laws of your state. I would also look into some kind of liability rider or umbrella policy with your home owner’s policy, which covers your personal liability and theft. Get your bike registered; wear your helmet, eye protection, whatever is required by state law so that if an accident occurs and you are at fault, there is no legal recourse. Even if you own a 750W/20mph ebike that meets the definition of a bicycle, any at-fault cyclist may still be denied coverage by stingy insurance companies who want to support their clients. Your health insurance will usually cover your medical bills, but the costs of an expensive ebike may be lost.

Ebike definition in Colorado follows the HR 727 National Law: Template:Convert e-power and Template:Convert max, 2 or 3 wheels, pedals that work. Legal low powered Ebikes are allowed on roads and bike lanes unless the city or county has passed laws to the contrary (Boulder city bans ebikes over 400W from bike lanes and all ebikes from bike paths) -none -(except Boulder city) have to date. Bicycles and Ebikes are disallowed on certain high speed highways and all Interstates unless signed as "Allowed" in certain rural Interstate stretches where the Interstate is the ONLY means of travel. [35] Unless the locality has specifically passed laws making ebikes illegal on sidewalks or trails, Ebikes are legal. However most business and shopping districts do not allow riding bikes or ebikes on sidewalks. Boulder and a few other cities specifically dis-allow ebikes on their trail systems through legal statute.
From the beginning and still today, bicycles have been and are employed for many uses. In a utilitarian way, bicycles are used for transportation, bicycle commuting, and utility cycling. It can be used as a 'work horse', used by mail carriers, paramedics, police, messengers, and general delivery services. Military uses of bicycles include communications, reconnaissance, troop movement, supply of provisions, and patrol. See also: bicycle infantry.
Most European bike rules are tight and restrictive. Right now the California state ebike rules in AB 1096 provide the clearest and cleanest format, and they support ebike riding. No other U.S. regulations come close. The big brand ebikes (Giant, Specialized, Trek) are selling bikes that fit within European rules (250w-300w motors). This gives them economies of scale. 

Electric powered bicycles slower than 20 km/h without pedaling are legally recognized as a non-mechanically operated vehicle in China.[32] According to "TECHNOLOGY WATCH", this should help promote its widespread use.[33] Electric bicycles were banned in some areas of Beijing from August 2002 to January 2006 due to concerns over environmental, safety and city image issues. Beijing has re-allowed use of approved electric bicycles as of January 4, 2006.[34] Some cities in China still ban electric bikes.
Choose a 36- or 48-volt battery with a capacity of 10Ah or 20Ah. Choose a battery designed for use on an electric bicycle, as it will come with a charger and be much easier to install. Make sure the voltage and capacity of the battery you choose is compatible with the conversion kit you purchased. The higher the voltage of your bike's battery, the more powerful your bike will be. When building an electric bike, choose a 36- or 48-volt battery to allow for speed and comfort.[5]

Since 2000, Canada's Motor Vehicle Safety Regulations (MVSR) have defined Power Assisted bicycles (PABs) as a separate category, and which require no license to operate. PABs are currently defined as a two- or three-wheeled bicycle equipped with handlebars and operable pedals, an attached electric motor of 500W or less, and a maximum speed capability of 32 km/h from the motor over level ground. Other requirements include a permanently affixed label from the manufacturer in a conspicuous location stating the vehicle is a power-assisted bicycle under the statutory requirements in force at the time of manufacture.[14][15] All power-assisted bicycles must utilize an electric motor for assisted propulsion.
With a chain drive transmission, a chainring attached to a crank drives the chain, which in turn rotates the rear wheel via the rear sprocket(s) (cassette or freewheel). There are four gearing options: two-speed hub gear integrated with chain ring, up to 3 chain rings, up to 11 sprockets, hub gear built into rear wheel (3-speed to 14-speed). The most common options are either a rear hub or multiple chain rings combined with multiple sprockets (other combinations of options are possible but less common).
Bicycles and horse buggies were the two mainstays of private transportation just prior to the automobile, and the grading of smooth roads in the late 19th century was stimulated by the widespread advertising, production, and use of these devices.[9] More than 1 billion bicycles have been manufactured worldwide as of the early 21st century.[1][2][3] Bicycles are the most common vehicle of any kind in the world, and the most numerous model of any kind of vehicle, whether human-powered or motor vehicle, is the Chinese Flying Pigeon, with numbers exceeding 500 million.[1] The next most numerous vehicle, the Honda Super Cub motorcycle, has more than 60 million units made, while most produced car, the Toyota Corolla, has reached 35 million and counting.[4][5][6][32]

But the whole is also influenced by the sensory systems which are very different from model to model. E.g. A typical 2013 Panasonic system requires pedalling for optimal support (55/minute?) and has both a pedalling frequency and a speed sensor. You don't get much assistance if you pedal very slowly or very fast. Typically, a rear motor has a force sensor, i.e. you get lots of support fast when you start pedalling in a low gear, i.e. it will "feel" your need for assistance.
This dexterous electric dirt bike is recommended for anyone over the age of 14. It’s fitted with double suspension and big tyres to help you tackle tough terrain. You also get a good selection of gears, that gives you optimal control. The Razor can go as fast as 15 mph on average, and comes with an excellent braking system. The aesthetics are on point, and the racer look is sure to impress. Don’t forget your helmet!
The electric bike revolution has officially crossed into the arena of off-road motorbikes. For those who prefer riding in nature, Cake introduced a product which not only respects the environment but other riders, as well. Cake’s Kalk is a silent off-road motorbike that releases no emissions into the atmosphere. Additionally, its electric motor means no gear changing or clutching — a silent motorbike that won’t detract from the experience of others. Perhaps the best part is Cake avoided any sacrifice in performance. The Kalk reaches speeds of fifty miles per hour and features three distinct driving modes: Discover, Explore, and Excite.

It appears Tennessee has not passed any legislation that applies to electric bicycles. Some people think the laws pertaining to a Motorized Bicycle should be used for an electric bicycle. However, a Motorized bicycle would be a gasoline powered device per state law as it is defined as "means a vehicle with two (2) or three (3) wheels, an automatic transmission, and a motor with a cylinder capacity not exceeding fifty cubic centimeters (50cc) which produces no more than two (2) brake horsepower and is capable of propelling the vehicle at a maximum design speed of no more than thirty miles per hour (30 mph) on level ground." [56]

An anti-theft radio GPS that mounts to standard bottle cage bosses and can locate within 9 feet, it runs on the Verizon network and costs $5/mo in addition to the hardware. Integrated vibration sensing alarm sends an automated text message alerting you anytime the bike has been "locked" using the companion smartphone application (Android or iOS)...

Both the Stromer and the Stoeckli are very nice looking designs and easy to handle. Reliability for both does not seem to be up to Swiss standards, e.g. some of the 2012 Stöcklis seem to have bad contacts. However, as of 2013, most of these problems should be fixed. The Cube got criticized for its battery/saddle system, but this has probably been fixed in more recent edition and it has less "punch" then the other's since the motor is smaller (324W?). I don't know about the BH Neo Nitro. Given the relatively low price of the BH Nitro, it may be the best buy in this category if you plan to cover smaller distances (the battery is limited to 9Ah, and Spain's industry does need some help ;) Anyhow, all of these models come with a variety of motors and country-specific modifications. E.g. in France, the BH Nitro comes with a 350W motor and is electronically limited to 25km/h, whereas in Switzerland you either can get a 500W - 45 km/h version or a 250W? - 25km/h version.
Electric bikes aren’t just a practical and environmentally conscious solution to gridlock, they also are really fun to ride. On top of all of the persuasive arguments to get an electric bike, I think the Rad Wagon’s best-selling point comes down to enjoyment. Zooming down the street each morning I wasn’t angrily yelling at fellow drivers or rushing not to be late. The bike commute was part of the journey each day, and not just the means I used to get around. There’s a reason so many people loved biking as a kid, and it can be just as fun as an adult.
European Union directive 2002/24/EC exempts vehicles with the following definition from type approval: "Cycles with pedal assistance which are equipped with an auxiliary electric motor having a maximum continuous rated power of 0.25 kW, of which the output is progressively reduced and finally cut off as the vehicle reaches a speed of 25km/h (15.5mph) or if the cyclist stops pedaling." This is the de facto definition of an electrically assisted pedal cycle in the EU. As with all EU directives, individual member countries of the EU are left to implement the requirements in national legislation.
In Quebec power-assisted bicycles are often classified similarly to standard pedal bicycles. They do not have to meet the conditions defined within the Canadian Motor Vehicle Safety Regulations (they are not classed as "motor vehicles"), but they do have to comply with federal regulations that define Power Assisted Bicycles. The Quebec Highway Safety Code defines a power-assisted bicycle as a bicycle(2 or 3 wheels that touch the ground) with an electric motor with a maximum power of 500W and a top speed of 32 km/h bearing a specific compliance label permanently attached by the manufacturer[30]. PABs are permitted on the road in the province of Quebec, but riders have to be 14 and over to ride the electric bicycle and if they're under the age of 18, must have a moped or scooter license.
Electric-assisted bicycles are treated as human-powered bicycles, while bicycles capable of propulsion by electric power alone face additional registration and regulatory requirements as mopeds. Requirements include electric power generation by a motor that cannot be easily modified, along with a power assist mechanism that operates safely and smoothly. In December 2008, The assist ratio was updated as follow: