What common forms of deice and anti-ice exist and what future alternatives are being researched?
In general, deicing (removal of ice after it had formed) and anti icing (prevention of ice formation) methods used are:



Image from GKN Technology: Leading the way toward more efficient aircraft


Mechanical which simply pushes the ice off the leading edges. An example is the pneumatic deicing boots, which is the oldest method used where an inflatable rubber boot is used for removing accumulated ice from the leading edges.




Source: quora.com

"Deicer (PSF)" by Pearson Scott Foresman - Archives of Pearson Scott Foresman, donated to the Wikimedia Foundation→This file has been extracted from another file: PSF D-240001.png.. Licensed under Public Domain via Commons.


Heating In large aircraft, the wing (and tail) leading edges are heated by engine bleed air (electro-thermal heaters in case of Boeing 787) for anti-icing and de-icing.




Image from Aircraft Anti-Icing Systems by Leslie Mehl and Annie Parsons


Chemical de-icing systems use dry or liquid chemicals designed to lower the freezing point of water (various salts or brines, alcohols, glycols); or by a combination of these different techniques.
Fluid de-icing systems which use de-icing fluid from a storage tank and fed through micro-filters to a number of porous metal distributor panels. As the fluid escapes, it breaks the adhesion between the ice and the wing and the airflow carries it away, creating the so called 'weeping wing'


There are a number of other de- and anti- icing methods are also available/under development, such as:


Electro-impulse method used high-voltage capacitors, which are rapidly
discharged through the coils installed just inside the skin of the aircraft leading edge, resulting in a electromagnetic repulsive force (on the aircraft skin), throwing ice in all directions. However, the electromagnetic interference and structural fatigue associated with this method limits its application.
Electro- Expulsive Separation System An electric current runs through parallel layers of flat, copper ribbon. When a large pulse of current is passed, a repelling magnetic field is created, causing the upper conductor to jump less than a twenty-thousandth of an inch. The resulting high acceleration causes the the ice to break into tiny particles that fall from the airplane's surface.




Electro-Expulsive Separation System shatters and ejects ice from a wing model in a wind tunnel test from ipp.nasa.gov


Electro-Mechanical Expulsion Deicing System, whose principle of operation is given by the developer as,



  A microsecond duration high current electrical pulse delivered to the actuators in timed sequences generates opposing electro-magnetic fields that cause the actuators to change shape rapidly. This change of the actuator shape is transmitted to the erosion shield of the LEA causing it to flex and vibrate at a very high frequency. This rapid motion results in acceleration-based debonding of accumulated ice on the erosion shield.




Image from An Overview of the Deicing and Antiicing Technologies with prospects for the Future by Zdobyslaw Goraj


Ultrasound Some research is also going on into vibrating the wings using ultrasound to remove ice formed.
Shape memory Alloys have also been proposed to be utilized for deicing and anti icing, with their shape changing properties being used for ice removal when required.




Image from An Overview of the Deicing and Antiicing Technologies with prospects for the Future by Zdobyslaw Goraj

There has also been some research into usage of carbon nanotubes for this purpose.