Between all of the different arcane spellcasters in Dungeons & Dragons 5th edition, the optional spell list can get long and confusing. Plus, not all spell lists share the same spells, so how are players supposed to know the difference between plain old "fun" spells, and spells that are absolutely invaluable to every player?
Thankfully, there's a short list of spells that every player can (and should) take into consideration when picking out their spellcaster's unique magical arsenal. Interestingly, most of these spells are relatively low-level; it just goes to show that Dungeons & Dragons spells don't need to be level 9 to be considered powerful.
Charm Person
Charm Person is universal for arcane spellcasters, and it's easy to see why: this spell is universally useful in just about any situation. Used at the right time in combat, it can stop an incoming hit in its tracks and even disrupt the unity within a group of enemies. Outside of combat, it's great for tricky social situations and even more likely to work, given that targets get advantage when in a battle but otherwise must simply make their wisdom saving throw. Toss in a spell such as Bane, which imposes disadvantage on a saving throw of choice, and spellcasters can have every NPC in the area bending to their will. Whether or not that's a good thing, on the other hand, is entirely up to the party.
Counterspell
It's a widely accepted fact at this point that magic is the most powerful thing in the world of D&D 5th edition. Yes, twenty swings of a great-ax are most definitely devastating for any character or monster, but there's just no denying that anyone who can lob level 9 fireballs at their enemies is probably the most dangerous force on the battlefield--at least, until that fireball is depleted. And that's exactly why at least one member of every D&D party should have Counterspell at the ready once they gain access to level 3 spells.
High-level damage spells are deadly, even when dealing half-damage to those who make their saving throws. But there's only one instance where those high-level spells don't have to be deadly at all, and that's when they're canceled out by a well-placed Counterspell. It interrupts a spell being cast; when successful, Counterspell causes that spell to fail entirely (and the spell slot is still used up, so it counts as something the enemy has cast). It doesn't matter if the interrupted spellcaster is a low-level apprentice or an actual god: if Counterspell takes effect, then their own spell becomes utterly useless. So, it should be pretty obvious why Counterspell is considered a life-saver.
Find Familiar
Now, some might argue that Find Familiar isn't universally available to all arcane casters--sorcerers, unfortunately, miss out on the fun by default. But here's the delightfully flexible truth of D&D: pretty much anything is attainable for those who want it, and this holds true for familiars as well. All sorcerers (and any other class, really) would have to do is take a feat like Ritual Caster or Magic Initiate, and voila! An animal friend is at the ready.
As to why Find Familiar comes so highly recommended, well, they're able to grow alongside their summoner and carry out tasks that a regular old pet would find quite impossible. Familiars can serve as spell conduits in battle, getting close enough to an enemy or a certain range for the spellcaster to release their spell through the familiar. That means squishy little spellcasters don't have to risk their necks every time they want to cast spells with a range of "touch," be it a damaging or a healing spell. Familiars are also perfect scouts, especially in situations when even the party's natural scout is a bit leary of venturing forth alone; spellcasters can take stock of the world through their familiar's eyes, and the familiar can quite literally be quiet as a mouse, or capable of getting a birds' eye view of anything.
Fireball
There are plenty of gnarly (and awesome) damage-dealing spells out there that could be listed for spellcasters who want to pack a punch, but Fireball is in a category all its own. Starting at level 3, it deals 8d6 points of pure, raging fire damage, and those numbers then increase as the spell is cast at higher levels.
Yes, there are single-target spells that deal even higher amounts of damage, and other area-of-effect spells with similar amounts like Lightning Bolt, but Fireball is great in that it envelops all creatures within 20 square feet, sets the area itself on fire, and can be used to catch flammable objects too. Basically, it can just be a standard damage-dealing spell, but casters who want to exercise their skills can also get creative with Fireball's many uses. It's technically only a sorcerer or wizard's spell, so this is an instance where other arcane casters should search out a wand of fireballs, or rely on one of their class feats that allows borrowing from other spell lists.
Fly
Few players are lucky enough to play a tiefling (or sorcerer, druid, etc.) who sprouts wings, but for the rest, there's the Fly spell. Coming in at level 3, Fly grants up to 10 minutes of flight at a considerable speed of 60 feet per turn, which allows those in combat to get an aerial advantage on the battlefield, and those out of combat to reach areas they otherwise couldn't or find an otherwise creative solution to a problem.
Case in point, there will come a time in any D&D campaign where one, if not every player will find themselves thinking, "Flying would come in real handy right about now!" When the time comes, make sure the party's arcane spellcaster has their Fly spell ready to go.
Invisibility
There will always be a need for the Invisibility spell in D&D, regardless of the campaign setting, classes within the party, party level, or pretty much any other factor. Some might think that Invisibility isn't useful in battle since it immediately drops as soon as an attack is made, but how about getting in that crucial surprise round? Or granting the rogue a sneak attack they wouldn't otherwise get? When it comes to spells like Invisibility, their usefulness is all about how players think to use them. And it goes without saying that getting advantage to stealth while sneaking around under the invisibility spell is absolutely invaluable to any party.
Scrying
Scrying is a little higher level than the rest, but it's well worth the wait. Any arcane spellcaster can grab this spell without needing the help of a feat or magic item, and at least one spellcaster in every D&D party should absolutely grab it. The Scrying spell allows its caster to become a super spy without even needing to get out of bed; casters can focus on a person or location that they know of, and get up to 10 minutes of full eyes and ears on that target. It's a form of magical tracking and spying that can be used in the case of slippery or difficult targets. Truly, Scrying can be the difference between a party gleaning life-saving knowledge of a combat encounter before walking into it...or not.
Shield
Nobody likes having their precious, painstakingly-built D&D character die, right? And unfortunately, being a spellcaster automatically means being at least a little easier to kill than pretty much any other class. Sure, a good sorcerer or wizard build should buff up on the constitution and dexterity to some degree, but there's still a natural disadvantage when it comes to all of the arcane spellcasting classes. It's probably something to do with the character being able to wield great and terrible cosmic power at their fingertips; there's got to be a trade-off.
So that's where the Shield spell comes in handy. It's not easy to have a high armor class all the time as a spellcaster, given the lack of armor they generally have, and harder still to have tons of hit points (that's reserved for barbarian builds, after all), but in a tight spot all they really need is a decent shield. The Shield spell takes the form of a reaction and can be cast immediately after being "hit" by an attack; until the start of their next turn, the caster gets a +5 bonus to their armor class. Plus, Shield can also be cast in response to the Magic Missile--another old faithful from the wizard's arsenal.
All in all, players should feel free to pick out whichever spells they feel would fit the character, be those strategy-based picks or spells chosen purely for the roleplaying potential. Still, the eight spells above would make for an incredibly solid foundation, and players are guaranteed to find endless uses for them during gameplay. Each of these spells offers its own sort of evidence as to why exactly arcane spellcasters in Dungeons & Dragons are the most feared adversary on any battlefield.