Random: Good for hordes of brainless thugs and animals who might attack indiscriminately, this is the simplest and one might argue fairest of solutions. Roll a die to determine who gets attacked (most parties correspond to 1d4, for example). Done. It will create illogical results you'll often want to fudge (10 opponents can't easily gang up on a single individual while leaving another free to move around, and so on), but it does have one advantage, even if it's just a perception. Rolling dice as a prologue to a battle's initial match-ups makes the players think the GM isn't singling anyone out specifically. It's just bad luck if they are targeted more than another player. And that perception can certainly help alleviate tension at the table, especially with touchier "cry foul" players.
Artificial Intelligence: Logic over fairness, and something both gamists and narrativists should strive for, each in their own way because it's not true that people, animals or monsters attack people randomly, without a shred of strategy or instinct. Giving different monsters/enemies different strategies deepens the game world and makes it feel more real, while simultaneously creating different challenges for the players. GMs should think about an overall strategy for any given encounter, one that fits the opponent(s), and then based on the opponent's intelligence and innate flexibility, allow them to adapt to the players' own actions. Not all opponents fight to the last man, or run when pressed, or necessarily attack the lead character, or the weakest, or the strongest. Do they respond to taunts? Can they be manipulated into attacking one person instead of another? Figure it out based on their particular point of view. And recurring villains not only know a party's abilities, but probably have an axe to grind with one or more of its members. These need not even be recurring; they might spring from a character's back story. Where revenge is concerned, balance and strategy might go out the window.
Artificial Balance: It's a game, and you want all the players to enjoy themselves. Once we acknowledge that it's a game and that's its purpose, we can allow for a combination of these two methods that doesn't leave any player wanting for action. Obviously, this will entail work at the design stage as well. The party's fighter may be able to handle that band of orcs, but it might be more interesting for the wizard if the band was accompanied by some kind of shaman. Superhero games frequently offer villainous teams whose members will pair up against PCs they are uniquely matched with. No one wants to stand around when a PC and NPC fight mano e mano. Early practice encounters shouldn't be difficult and lethal, then the climax too easy. If you've structured your scenario correctly, then you'll have challenges for each of the characters in each of the encounters (and these need not be combat-oriented; perhaps there's a way to end the fight if only the thief can get up to the ceiling and rip the soul-gem out of its fixture, who knows). Dice or strategies that don't take the exact composition of a party might not do that.
Karmic: In the more narrativistic arena, some PCs simply "asked for it". Maybe they acted badly and deserve the aggro they're generating. They "angered the gods", so to speak. Perhaps they're involved in a subplot that, in a story sense, requires them to be tested in some way. And perhaps their role in the story is to be the punching bag, the unlucky sod who's always getting swamped by non-lethal attacks, the butt of the joke. It's a game, but it's also a collaborative story. Sometimes, you have to give in to that.
Location, Location, Location: If you're using miniatures, a lot of these decisions are taken away from you. Line of sight, who can get access to whom, movement rates, etc. will dictate what's possible and logical (which doesn't mean opponents should have no strategy going in). Even without miniatures, sometimes you'll want to exploit a cool location to its fullest. You don't want your climax to feel like it's being fought in a large empty room. By allowing players to visualize a location's opportunities - which means also telling them where the opponents are in the space - you'll restrict, but hopefully also create cool opportunities for, what can happen in combat.
Obviously, most GMs will use a combination of these depending on the situation. What technique(s) do YOU use?