Class levels
The Hexblade Warlock's Accursed Specter feature allows a hexblade to create a specter once per day.
Magic Items
Magic items are kind of a mixed bag, and once you get up to artifact rarity, basically anything can happen..
The Teeth of Dahlver-Nar, for example, do... a lot of things. Some of them include summoning various undead. Similarly, Luba’s Tarokka of Souls. The Wand of Orcus is more limited (except when held by Orcus, see below.)
The Deck of Many Things can summon an Avatar of Death, which is itself undead. How this can be used tactically is a bit questionable.
Monsters
There exist several non-undead monsters that can create undead creatures without spellcasting.
Orcus
It's easy to pass over Orcus for this question, because at first glance the demon lord is just using spells such as animate dead and create undead (and in fact has features that enhance his uses of those spells). However, Orcus also has an action granted to him by his Wand of Orcus:
While holding the wand, Orcus can use an action to conjure undead creatures whose combined average hit points don’t exceed 500. These undead magically rise up from the ground or otherwise form in unoccupied spaces within 300 feet of Orcus and obey his commands until they are destroyed or until he dismisses them as an action. Once this property of the wand is used, the property can’t be used again until the next dawn.
This is a heightened property of the wand itself, distinct from its ability to cast animate dead, since in anyone else's hands it can only create zombies and skeletons. In addition, the regional effects of Orcus's lair and his lair actions can create undead without duplicating the effects of spells.
Shadow Dragons
Any dragon created with the shadow dragon template (such as the eye-wateringly-named Karkethzerethzerus, the Sable Despoiler) can raise creatures killed by its Shadow Breath as undead shadows.
...And Others
Other monsters can reanimate those they kill, such as:
...while others have more exotic methods, such as the Maurezhi's ability to re-reanimate undead that have been killed.