The commander's owner gets to choose. If a commander would go to the graveyard, exile, library, or hand from anywhere, the owner can choose to put it in the command zone instead.
So you know: whether or not the effect in question is either something like Oblivion Ring or Banishing Light actually matters. If the the owner lets the commander go to exile, then it will return to the battlefield in either case if the Ring/Light card leaves the battlefield. If the owner puts the commander in the command zone instead, then a Ring-like effect won't bring it back to the battlefield (there's no "exiled card" to be returned), but a Light-like effect will (the card moved to a public zone and the effect doesn't specify "the exiled card" gets returned).
March 12, 2018 11:23 a.m.
Rhadamanthus So exiling their general wouldn't get rid of it until the enchantment leaves the battlefield?
March 12, 2018 1:52 p.m.
To go off on a bit of a tangent, there are enchantments that will remove a commander until the enchantment is destroyed: Song of the Dryads, Darksteel Mutation, and Imprisoned in the Moon. Unlike Oblivion Ring and its ilk, these enchantments do not force the commander to change zones, thus do not give your opponent the option of returning the commander to the command zone.
March 12, 2018 2 p.m.
For some reason I feel like I don't totally understand the follow-up question. Let me know if I'm on the wrong track.
If the commander's owner allows the commander to be put into exile, then the Oblivion Ring/whatever will work normally. The creature stays in exile until the Ring leaves the battlefield. It can't be cast from exile.
If the commander's owner chooses to put the commander into the command zone instead of exile, then they can cast it later if they want to. It doesn't stay locked up by the Ring.
March 12, 2018 2:23 p.m.
Another difference between Oblivion Ring effects and Banishing Light effects is that because Oblivion Ring returns using a trigger, if the player controlling Oblivion Ring leaves the game (ie. loses) the ability cannot be added to the stack so the commander stays exiled forever (though most of the time they'll just send the commander to the command zone anyways). Because Banishing Light is a limited duration effect, if the player controlling it leaves the game, the duration ends, and the commander immediately returns to the battlefield from whatever zone they were sent to (if they are still there).
March 12, 2018 5:03 p.m.
903.9. If a commander would be exiled from anywhere or put into its owners hand, graveyard, orlibrary from anywhere, its owner may put it into the command zone instead. This replacement effectmay apply more than once to the same event. This is an exception to rule 614.5.
So the choice what will happen to the commander in question, depends entirely on the decision from the owner.
Note: if you would let your commander be exiled by Oblivion Ring and the triggered ability that would return the exiled card to it's owner's control would get countered, you'll be unable to play you commander for the rest of that game UNLESS you have something that allows you to retrieve it from the exile zone like Pull from Eternity.
March 12, 2018 5:32 p.m.
@Rhadamanthus The replacement effect only applies to exiling or destroying a creature
@Snap157 Mark an answer as accepted so this question gets moved
March 13, 2018 6:43 a.m.
@Spirit_Logan The replacement effect applies to going to the graveyard, exile, library, or hand, from any zone. It especially does not simply refer to "destroy" as if the commander would go to the graveyard due to being countered, sacrificed, having toughness 0 or less, discarded, or any number of other actions that aren't "destroyed," it still applies.
March 13, 2018 12:28 p.m.
@Spirit_Logan: This rule has changed a couple times over the last several years, so you're probably thinking of an earlier version of it. See XownagerX's post for the most up-to-date version of the rule.