To counter a spell, expend one prepared spell and follow the formula presented for dispell magic:
Dispell Magic: Unless countered, this spell will be effective in dispelling enchantments of most kinds (referee’s option), except those on magical items and the like. This is modified by the following formula. The success of a Dispell Magic spell is a ratio of the dispeller over the original spell caster, so if a 5th level Magic-User attempts to dispell the spell of a 10th level Magic-User there is a 50% chance of success. Duration: 1 turn. Range: 12″.
Source: Men & Magic, page 25.
That is, any prepared spell can be “converted” into an antagonistic dispell magic. One could without issue probably extend that to full dispell magic functionality (thereby doing away with the need to find, learn, or prepare dispell magic as a distinct spell), given that removing enchantments is a relatively core aspect of wizarding, though I could understand wanting to keep the full dispell magic a separate thing.
Note that OD&D does this differently than AD&D, which works like the BRP resistance table (50% success modified by level differential). To make the difference clear, in OD&D a 9th level magic-user has a 90% chance of successfully dispelling an 10th level magic-user’s enchantment (9/10), while in AD&D the chance would be only 45% (50% -5% for having one less level).
Alternatively, compare spell levels rather than class levels using the OD&D formula. So, expending a second level spell in an attempt to counter a third level spell would have a 2/3 (66%) chance of success. This method might be preferred if you see the countering process as an opposition of specific spell energies rather than a contest between the overall skill of the two magic-users.
The burn spells paradigm is becoming increasingly attractive to me. There is some danger of complexity creep, so the possibilities should be limited to a small number of effects. That said, having several default options frees up magic-users to prepare more obscure or interesting spells, which otherwise might not get as much use, much as 3E clerics were able to convert any spells into cures. Further, requiring the expenditure of prepared spells to power such effects retains some degree of resource constraint, unlike make other unlimited or at-will approaches, and doesn’t require tracking any additional information, since spell slots are already managed.
The options so far that I have thought about are maleficence, magical defense, and now dispell magic. I could see adding read magic to that list perhaps, though I am also experimenting with replacing read magic with a “skill” type d6 roll that comes at the cost of an exploration turn.
(This idea came to me when I repurposed dispell magic for banishing summoned creatures.)