The basic steps with examples of the free-radical addition (also known as radical chain mechanism) are:
Free-radical reactions depend on a reagent having a (relatively) weak bond, allowing it to homolyse to form radicals (often with heat or light). Reagents without such a weak bond would likely proceed via a different mechanism. An example of an addition reaction involving aryl radicals is the Meerwein arylation.
To illustrate, consider the alkoxy radical-catalyzed, anti-Markovnikov reaction of hydrogen bromide to an alkene. In this reaction, a catalytic amount of organic peroxide is needed to abstract the acidic proton from HBr and generate the bromine radical, however a full molar equivalent of alkene and acid is required for completion.
Note that the radical will be on the more substituted carbon. Free-radical addition does not occur with the molecules HCl or HI. Both reactions are extremely endothermic and are not chemically favored.
In one specific type of radical addition called self-terminating oxidative radical cyclization, alkynes are oxidized to ketones with intramolecular radical cyclization and the radical species are inorganic rather than carbon based. This type of reaction is self-terminating because propagating is not possible and the initiator is used in stoichiometric amounts.
As an example a nitrate radical is generated by photolysis of CAN which reacts with an alkyne to generate first a very reactive vinyl radical and then via a 1,5-hydrogen atom transfer (HAT) and 5-exo-trig ring-closure a ketyl radical. The ketyl dislodges a nitrite radical which is not reactive enough for propagation and the ketone is formed.