In what ways can a Non-paladin access Paladin spells?

Question

What different options are available (in the published materials of D&D 5e: rulebooks, UA, etc) for a Non-paladin to access Paladin-specific spells?

Notes

• Only spells that are unique to the Paladin spell list (i.e. only spells that are not freely available on another class' spell list)
• Features that grant access to One Specific, Any, or All spells from the Paladin list
  • Example: Divine Soul lets Sorcerers choose spells from the Cleric spell list

Answer 1

The following is a list of the ways I could find

The Bard's Magical Secrets feature allows them to gain spells from any class' spell list so this would work. At 10th level, when they gain this feature, they can already cast 5th level spells so they could select any and all Paladin spells.

You can also use a Ring of Spell Storing to allow anybody to cast any Paladin spell. This would work because the ring can store up to a fifth level spell which is the highest level spell Paladins acquire.

The wish spell can be used to duplicate any spell of 8th level or lower, which would include all Paladin spells.

There are a number of monsters that know (or can cast) Paladin exclusive spells, theoretically befriending or resurrecting one of these monsters gives you access to these spells. As user @NathanS points out, we could also true polymorph into one of these monsters to gain the use of their spells.

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There are a number of Paladin exclusive spells (note that I will not list spells that only an older version of a class or subclass got, such as something only the UA Artificer got that the final one did not):

• Aura of life:

  An Undying Warlock, a Solidarity Cleric (from Plane Shift: Amonkhet), an Unearthed Arcana Twilight Cleric, and an Unearthed Arcana Wildfire Druid as well as the Selesnya Initiate background from Guildmasters' Guide to Ravnica. The Unearthed Arcana variant class Cleric also gets this.

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• Aura of of purity:

  A Battle Smith Artificer, and an Unearthed Arcana Unity Cleric. The Unearthed Arcana variant class Cleric also gets this.

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• Aura of vitality:

  A Battle Smith Artificer, and an Unearthed Arcana Twilight Cleric. The Unearthed Arcana variant class Cleric and Druid also get this.

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• Banishing smite:

  A Hexblade Warlock and the Battle Smith Artificer.

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• Blinding smite:

  An [Unearthed Arcana Revisited Battle Smith Artificer][2], an Unearthed Arcana Stone Sorcerer, and the Boros Legionnaire background from Guildmasters' Guide to Ravnica. The Unearthed Arcana variant class Ranger also gets this.

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• Branding smite:

  A Hexblade Warlock, A Battle Smith Artificer, an Unearthed Arcana Stone Sorcerer, and the Zariel Tiefling from Mordenkainen's Tome of Foes. Also the Necklace of Prayer Beads item from the Dungeon Master's Guide. The Unearthed Arcana variant class Cleric also gets this.

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• Circle of power:

  The Solidarity Cleric (from Plane Shift: Amonkhet) and the Unearthed Arcana Twilight Cleric.

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• Compelled duel:

  The Unearthed Arcana Protection Cleric, the Unearthed Arcana Stone Sorcerer, and the Gruul Anarch background from Guildmasters' Guide to Ravnica. Also the Gruul Guild Signet item from Guildmasters' Guide to Ravnica.

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• Crusader's mantle:

  The War Cleric and the Solidairty cleric from Plane Shift: Amonkhet. Also the Lost Sword item from Curse of Strahd.

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• Destructive wave:

  The Tempest Cleric, the Strength Cleric (from Plane Shift: Amonkhet), and the Zeal Cleric (from Plane Shift: Amonkhet). Also the Gruul Anarch background from Guildmaster's Guide to Ravnica

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• Divine favor:

  The War Cleric and the Strength Cleric (from Plane Shift: Amonkhet).

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• Find greater steed:

  There is no way to get this spell besides the methods (or similar ones) listed at the top.

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• Find steed:

  There is no way to get this spell besides the methods (or similar ones) listed at the top.

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• Searing smite:

  The Forge Cleric, the Unearthed Arcana Stone Sorcerer, and the Zeal Cleric (from Plane Shift: Amonkhet). As well as the Zariel Tiefling from Mordenkainen's Tome of Foes. The Unearthed Arcana variant class Ranger also gets this.

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• Staggering smite:

  The Hexblade Warlock, and the Unearthed Arcana Stone Sorcerer.

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• Thunderous smite:

  The Unearthed Arcana Stone Sorcerer and the Zeal Cleric (from Plane Shift: Amonkhet).

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• Wrathful smite:

  The Hexblade Warlock and the Unearthed Arcana Stone Sorcerer. The Unearthed Arcana variant class Cleric also gets this.

Answer 2

To some extent

If you mean being able to cast all paladin spells inherently then there isn't really a way.

Bards get an ability called magical secrets which lets them acquire spells from other classes. They could obtain some paladin spells this way.

If you have a paladin in your party and a ring of spell storing (or equivalent) then you could have the paladin cast their spells into the ring for you to cast.

For spells that are available on other class spell lists you could use the above methods or take class levels in the classes that gains access to those spells. I don't consider that to be much of a solution as, by the same logic, you could just take levels in Paladin to achieve the same effect.

Some magical items can give you access to certain spells on the paladin list. eg. a Necklace of Prayer Beads.