Recently, I wrote about an interception system which allows characters to defend allies by blocking incoming attacks. Interception belongs to a broader category of actions that can be taken out of turn. Each broad class group has it’s own type of reaction. Magic-users may try to disrupt enemy casters with counter-spells and thieves may take opportunistic actions.
Counter-spell. There are many different ways of resolving counter-spells, but the important point here for magic-users is that they don’t need to hold an action to be able to attempt a counter. They get one for free. Whether a counter-spell should require some sort of resource cost (maybe burning a spell?) depends primarily on the magic system. A simple “attack roll” system would work well for trad D&D if you want to decrease the opportunity cost of using a counter-spell (1d20 + half-level + int bonus >= 10 + enemy spell level, for example).
Opportunism. This kind of action may be used for something like an attempt to grab a pouch from the belt of a passing enemy. Perhaps a dexterity check is required for success depending on the action in question. Remember that this is a reaction, not a free action.
Characters may not take more than one reaction per turn, and only primary PCs (not retainers) may use reactions. This rule is to decrease potential complexity and to mitigate any game slow-down caused by extra actions. It is not expected that reactions will be relevant during every combat round.
Clerics, being a species of fighter/mage, could (at character creation time) choose either the intercept or counter-spell reaction type. Intercept would be more appropriate for crusader style clerics, whereas counter-spell might be useful to a witch hunter.