From Distillers Wiki
The entire still operation depends on the contents of the boiler being boiled so that vapors can rise up the column. It is desirable to be able to be control heat somewhat finely. This heat can come from a kitchen stove or hot plate for a small still (however there will be problems with the elements cycling on and off too slowly); while a larger still is usually heated by a propane/lpg burner or an electric water heater element installed inside the boiler. The heat input required for efficent operation depends on the diameter of the column. 2000W is sufficent for 2" (50mm) reflux columns, but more is needed for larger columns in proportion with the increase in the area of the column, so a 3" will need roughly double that. It is important not to overpower reflux columns, as at best it will wreck the packing's effectiveness, and at worst the still could choke and puke, pushing large amounts of hot liquid out the top of the column. For a pot still, heat requirements are more flexible, but generally, more is better, especially for stripping runs, and heat control is essential for spirit runs.
The considerations for using a kitchen stove to heat the boiler depend largely on height restriction and power. There needs to be sufficient space between the kitchen stove and the ceiling for the entire still. You also need to have enough power to heat up the contents of your boiler in a timely fashion and maintain a good boil. Anything over a 5 gallon boiler would severely tax most common kitchen stoves. There will also potentially be problems with the element cycling on and off too slowly to provide the steady heat that reflux distillation needs, and this cycling will also cause a pot still to surge.
Electric immersion elements provide a good source for heat and can be procured from common water heaters or hardware stores in a range of power rattings. There are also stainless steel elements designed for beer brewers, that often have weldless instalation. These heaters are designed to sit inside the boiler and heat the contents of the boiler directly. This type of heater requires mounting in the wall of the boiler and must be sealed so that the contents of the boiler won't leak out. The technique for mounting varies widely depending on the particular type of boiler and model of heating element you are using, but in the frequently seen keg boilers, welding a BSP fitting to use hot water cylinder elements is common, as is using a weldless flange kit.
The benefits of electric heating elements are that they are cleaner (no fumes or C02/CO emissions) and as such require less venting (it's still not a good idea to produce ethanol vapours in very confined spaces though) and are better suited to indoor use. They are safer (if wired correctly) since there is no open flame, minimizing the risk of explosion and alcohol fires. Some may find that the running cost of usage is cheaper than using propane in an open-flame set-up, but this will vary greatly by area.
The drawbacks of internal electric heating elements are that they may require a higher voltage outlet to operate if you are in the USA (120/240 AC), wiring connections should be enclosed in approved electrical boxes and, to be safe, the work must meet a lot of electrical code specifications. They require sealing where the element is installed in the boiler (unless a welded fitting is used) and if improperly done this junction could be subject to leaking. They also come in direct contact with the boiler charge, and if the wash is poorly cleared and has solids in it it can bake/burn onto the element requiring extensive cleaning, although this is very unlikely for the sugar washes that many distillers use. For precise control, electric elements will require a controller such as a phase angle or burst fire controller, or a solidstate relay and controller (see below). There is likely a greater initial cost and time investment to these setups. Low wattages may require extensive time to heat-up large volumes of mash, and accordingly some users have chosen to install a second element to speed-up the initial boiler heat-up process.
Alternatively, an external electric heating element, or hot plate, can be used. These work for smaller boilers but are usually limited to lower wattages (less than 1500 watts). External hot plates are much less efficient than direct contact internal heating, and like a stovetop, have the problem of slow heat cycling, so will likely require rewiring. These are probably best considered as a small (sub 2") still only option.
Electric controllers Purchasing such a controller can be prohibitively expensive. Alternatively, such a controller can be built with simple electronic skills at a very low cost:    
Natural gas, propane, and lpg can be used with a simple burner to heat the boiler directly. Burners range from 10,000 BTU up to 100,000 BTU. Gas Burners come in a wide range of sizes and styles, but all of them are meant to sit below and heat the bottom of the boiler  .
Gas has several advantages over electric. Gas controls are much more flexible "off the shelf" and allow for fine (if not accurate) adjustment to heat output. Most gas burners can also generate a higher maximum energy than electrical circuits can yield, giving much faster heat-up times. Gas makes the entire apparatus portable to areas away from power supply, which may be of use in sheds without utilities or outside. Many users already have some type of gas burner that can also serve their distilling needs without any extra modifications or need to purchase special equipment. Gas burners are probably less likely to scorch a thick boiler charge if run carefully, though some very high-solid washes will still require a slow heat up or indirect heat like a double boiler to prevent burning
The drawbacks are that an open flame puts off dangerous CO2 and CO and requires plenty of ventilation or must be used outdoors. Open flames from a gas burner can ignite alcohol vapors in the case of a condenser failure or even cause an explosion if leaks are not identified and the set-up isn't watched carefully. Gas/Propane costs can be much higher than using electricity (depending upon area) and may be more difficult to move or transport. Propane tanks also need to be refilled after several uses creating extra trips to the 'propane store', and can leave you short mid run. Gas is a more inefficent heat source, as the boiler is not as easily insulated as an electric boiler because of fire hazards and venting issues (see insulation. It is also harder to set a known wattage input with gas. It is possible, but requires some experimenting and measure water production at various settings to calculate. This means it can be hard to determine if a reflux column is running at its most efficient speed, but has little implication for pot stillers.