As far as in-game explanations, there's also the intervention of supernatural entities: gods, demons, nature spirits, etc. That could tie in with word-based magic -- incantations to call attention and beseech aid -- or not. The indie game
Sorcerer, for example, posits a demonic familiar for every sorcerer, disguised as an ordinary object, who lends the sorcerer power for a price.
As far as out-of-game-effects, you also have to consider a) whether PCs can use magic at all (except for one edition
Pendragon only allows non-magical knights and the occasional non-combat female character), and whether PC magicians are "balanced" against non-magical PCs or not. (In
Ars Magica, wizards are by far more powerful than mundanes. The game balanced this out by giving every character a wizard and a competent mundane, plus a pool of redshirt "grogs" as bodyguards. In a given adventure, players could choose to play their wizard, their mundane companion, or a grog.)
Most games treat magic as an "alternate technology", perhaps with unexpected effects like harming humans but not objects or vice versa. For some more radical possibilities, look at John H. Kim's essay
"Breaking Out of Scientific Magic Systems", which I recommend highly (and frequently).