Magic systems

Slot-based

Spells are prepared in advance, and once prepared a spell can be cast at anytime with little or no chance of failure, but once cast the spell is consumed; to cast a spell twice it has to be prepared twice, and so on.

Typically the maximum number of spells that can be prepared is finite, either with an explicit cap (i.e. 'Slots'), or by requiring a finite resource (i.e. Material components).

Obvious variations would be to have more powerful spells require more slots/resources, and D&D-style leveled slots.

Mana-Based

Spells consume a quantity of spellpoints (i.e. Mana) when cast, otherwise spellcasting is unrestricted.

Obvious variants are 'Aspected Mana' (Fire mana, water, defensive, aggressive, etc., and other more unusual divisions), to have spells consume things other things instead of mana (Hitpoints, material components, etc.), and to have spells consume more then one type of thing/aspect of mana (e.g. 3 fire mana and a stick of charcoal))

Chance-Based

Spellcasting is essentially free, but has a chance of failure, probably a very large chance.

Obvious variants is to have the chance of failure be affected by some combination stats, skill, or environment.

Furthermore, theres nothing wrong with combining the above, infact its quite common. A Slot/Mana system might let you memorize a shortlist of spells, which are then cast as a mana system. Crawl does this. A Mana/Chance system might allow skill to reduce the mana cost of casting spells. The Pen and Paper GURPS does this.