Four more superbly useful magic-user spells - and not a direct damage spell among them.
5. Haste: Super speed is often a useful ability, and in B/X, it lacks the penalty levied against it in AD&D (specifically, rapid aging) so you can use it with impunity as often as you're able to cast it. The doubled movement rate is nice, but of course the main attraction is doubling the rate of attacks. It affects up to 24 creatures (implying that the caster can choose which ones) within a 60' diameter circle, and at up to 240' range. (What's the deal with the crazy range, anyway?) This means that you can easily Haste the entire party, plus mounts and henchmen, even if melee has already begun.
In case it isn't obvious, let me just state it plainly: Doubling the attacks of an entire party, even a smallish one, is a huge advantage. Characters who have trouble hitting in combat get an extra chance per round to do so. Characters who hit easily can buzz through opponents in a whirlwind of steel and blood. Hey, at least it's not like AD&D or Mentzer D&D, where higher-level fighter-types get extra attacks, and then get those doubled by Haste. The only time you're likely to see that level of rules exploitation in B/X is when players stack the effect of the spell with the effects of items like a potion of speed. Even so, it might be a good idea to reinterpret the spell as providing an extra attack per round, rather than doubling attacks. Most of the time it's functionally identical, but when it isn't, it prevents crazy stuff like a warhorse getting four strikes per round or a pet bear getting six.
With such great offensive potential, the defensive use of the spell is easily overlooked. Doubling the movement rates of an entire party is a great way to beat a hasty retreat from a too-tough encounter.
Other tasks might be accelerated also. The rules specify that Haste does not increase the rate of spell-casting, so I interpret it as affecting only movement and reflexes, not thinking and cognitive functions. A repetetive task that requires no active thinking could be sped up this way, but it wouldn't allow you to read a book twice as fast, for instance. You could clear a passage of rubble in half the time it would normally take, but I wouldn't allow a thief to pick locks faster, because that involves more of the higher cognitive functions that aren't affected by Haste.
6. Hold Person: Though the description states that it's exactly like the cleric spell of the same name, it's actually a bit inferior in range and duration: 120' and 1 turn per level, vs. 180' and a flat 9 turns for the cleric version. I'm not sure if this is a deliberate design choice or just the result of the spells being written up separately, but these ticky-tack little differences between one version and another serve no purpose in my mind other than annoyance. It doesn't make arcane magic and divine magic feel different; it's just another set of numbers to look up.
Anyway...the spell itself is in all other respects as useful as the clerical version. Even slightly nerfed compared to that version, it's one that should make most players salivate over the possibility of acquiring.
7. Infravision: This might be the shortest spell description in the rules: "This spell enables the creature it is cast on to see objects in the dark to a distance of 60'." That's it. That's a bit simpler than the description of the infravision ability of dwarves, elves, and monsters as given in the Basic rules, but it's probably a safe assumption that that description applies to the spell effect as well.
Though the range is listed as 0, the description clearly implies that it's a touch spell rather than caster only, and it lasts an entire day! A magic-user could cast it on someone as a backup in case the party's light sources fail. Cast it on a thief or other stealthy character in order to scout ahead without betraying his presence with bright light. In a party with most of the fighting roles filled by dwarves and elves who already have infravision, it's conceivable that a magic-user with a couple level 3 spell slots could grant the rest of the party the ability and forego light sources altogether.
8. Invisibility 10' Radius: What's better than invisibility? Invisibility for the whole party, of course! This spell functions exactly as the 2nd level Invisibility spell (though apparently on creatures only - there's no mention of objects) except that the range is 120' including the semi-permanent duration. It also makes all creatures within 10' of the target creature invisible as well, as long as they remain within 10' and don't attack or cast spells (conditions which break the standard Invisibility spell, and presumably this one as well.) The description implies that creatures break their invisibility individually, i.e. one creature attacking becomes visible itself, but doesn't dispel the invisibility of the others.
One rather important detail that isn't stated is whether the creatures made invisible by the spell can see each other. If they can't, keeping within 10' of the central target creature, especially when that creature is moving, is problematic. It's probably easiest to rule that they can see each other, though it might be an interesting twist if a creature loses the ability to see the others if it breaks the spell on itself by attacking or moving too far away.
Naturally, Invisibility 10' Radius has all sorts of stealth, ambush, and escape applications. A circle 20' across is wide enough to encompass a small camp site, minimizing the chances of the party being attacked while resting. Turning the whole party invisible is a nice way to foil pursuit, too.
A potentially fun, if rather dastardly, trick which might be played with the spell is to have an attractive target visible in the middle, surrounded by invisible fighter-types. Won't those orcs who think they're ganging up on a squishy wizard be surprised?!