The B/X magic-user spell lists are 12 spells per level, and considerably more diverse than the cleric spells. For the purpose of these posts, I'll continue breaking the lists into tasty bite-sized chunks of four spells each.
1. Charm Person: This is one of the most powerful and useful spells a magic-user can have at low levels. Not only does it stand an excellent chance of taking an opponent out of a fight with a single roll, if it works you also have a loyal hench-creature, at least for a while. It isn't quite mind control; the description states that the creature will treat the caster like its best friend, protecting him from harm and generally obeying orders that don't contradict its nature too strongly and aren't obviously suicidal. These are important points. A charmed ogre or kobold or evil priest is not going to stop acting like an ogre or kobold or evil priest; they're just going to be eager to please the spell caster.
As the party reaches higher levels, the types of non-human creatures that can be charmed become less useful as combat allies, and the NPCs that would be useful get better at making saving throws. Even so, charming a low-level enemy isn't necessarily a waste. A charmed creature is a great source of information - there's very little it wouldn't tell its "best friend," after all. If it isn't brought along with the party, it could be released and allowed to go back to its own kind, effectively giving the magic-user a mole in the enemy camp for as long as the charm lasts. Naturally, Charm Person also has big potential in town phases of adventures when NPCs aren't as cooperative as the players might like.
The rules don't specify any limit to the number of creatures a caster can have under charm at once, so it's theoretically possible to accumulate a mob of goblin minions, or to have an entire hamlet under one's spell. Also unspecified is precisely what happens when a charm wears off. Does the creature immediately realize it's been had, or is it more of a head-shaking "What was I thinking?" moment? Either possibility has interesting implications.
2. Detect Magic: (Since this spell is identical to the cleric version, my thoughts here are just a direct copy/paste of what I wrote for that iteration of the spell, repeated here for convenience.)
Not a lot needs to be said about this one. Like Detect Evil, it causes
targets detected by it to glow; thus that information is available to
anyone with eyes to see it, not just the caster. With a range of 60'
and duration of 2 turns, a sizeable area can be scanned, and it might
prove useful to cast it before a major confrontation in order to know
which opponents are bearing enchanted equipment or magical enhancements
of some sort. Of course, clever opponents might deduce that the party's
own equipment that glows is magical too...
3. Floating Disc: Kind of a schizophrenic spell, a Floating Disc looks like the perfect way to haul around 500 pounds of loot, until you realize that it lasts a mere 6 turns (1 hour.) Perhaps you could get a heavy load of treasure from a single hoard to the dungeon entrance and arrange for it to be carted away from there, but it's not much good for walking around and gathering things bit by bit. It's good for carrying paralyzed or otherwise incapacitated characters around when there's no time to let the effect wear off. Combine it with a ring of water walking, and the magic-user becomes an instant ferry service. The disc might also serve as a platform for another character to stand on in order to reach some high spot. A magic-user could use it to help a heavily-laden fighter in an evasion-and-pursuit scenario - just have the fighter hop on the disc and let the unarmored magic-user run like hell at full movement rate with the fighter in tow. Come to think of it, having a companion on a floating disc would allow that character to face backward, firing missiles or slinging flaming oil to cover the party's escape without having to slow down.
More imaginative uses of the spell hinge on interpretation of a vague clause in the description: "The floating disc will be created at the height of the caster's waist, and will remain at that height..." Does the disc remain at the level at which it was created, or does it remain at the height of the caster's waist as the caster gains or loses altitude? The former severely constrains its usefulness even for the limited task of carrying heavy loot. What happens if the caster goes up or down stairs or a slope? Will the disc end up running aground when the caster ascends, or high above his head when he descends? It seems better (and more fun) to choose the latter interpretation, that the disc changes altitude to remain at the level of the caster's waist. Then, a magic-user who has access to levitation magic can function as an arcane elevator operator. Or, cast a Fly spell and take a buddy cloud surfing!
4. Hold Portal: Yes, it's kind of a one-trick pony, but it's a pretty useful trick when you need to shake pursuit, hole up in a room for a while, or keep a creature that you've chosen to release for whatever reason off your case until you're long gone. The duration is variable, at 2d6 turns, so you might get two hours or you might only get 20 minutes. Even the low end gives enough time to search a room, and ample time for putting some distance between you and the horde of screaming goblindom outraged that you just killed their king and looted his throne room. Creatures 3 or more HD above the caster's level can break through in one round, but a one round head start can still make all the difference between eluding a pursuer and getting caught.