I’m sure this has been answered before but I couldn’t find it. So both the oath spells and circle spells say that are always prepared and don’t count against the number of spells you can prepare each day. The PHB also doesn’t say anything about when those spells are relearned or reprepared, as in after a long or short rest. So because of that, and the fact that the PHB does say the spells are always prepared, does the paladin and Druid have an endless supply of those to cast?

No. The number of spells a paladin or druid can cast per day is limited by their spell slots. Their oath/circle spells are just always prepared, so they are always an option to cast with the spell slots.

 But it also says those spells don’t count against the number of spells you can prepare each day, so the oath/circle spells aren’t limited by your spell slots, they are in addition to them.   

There are two metrics with spellcasting

1. what spells you can cast for the day - these are "prepared"
2. how many spells you can cast - these are slots

As a druid, you don't have access to your whole spell list each day. You can only prepare a certain number of spells that you think you might use. Then you spend slots to use them. Things that are always prepared simply means you have a wider pool of spells available to spend your slots on.

Quote from xAMCx >>

 But it also says those spells don’t count against the number of spells you can prepare each day, so the oath/circle spells aren’t limited by your spell slots, they are in addition to them.   

There is a difference between Spell Slots and Spell Preparation. Prepared Spell list is the list of spells you have access to on a particular day. Spell Slots are the equivalent of MP in videogames.

If you have played Pokémon, Prepared Spell list is the equivalent of a Pokémon's move list, while Spell Slots are the equivalent of a move's PP.

The always Prepared Spells basically just means that your Paladin will always have access to certain Prepared Spells. It is the equivalent of Struggle in Pokémon which all Pokémon has access to, and you cannot get rid of Struggle unless you hack or something.

Got ya. That makes sense. And I realize now ftl essentially said the same thing.  Thanks guys

One thing to bear in mind is if any of the spells you have prepared can be cast as a ritual and if your character has the ritual caster ability. These spells you CAN cast as many times as you like a day. Unfortunately, I haven't seen many spells with the ritual tag that were of much use on my characters. 

Wtfdndad, what characters are you dealing with?

Wizards use ritual spells a lot.  I routinely use the following ritual spells:

1. Detect Magic, Identify, Comprehend Languages, and Find Familiar
2. Skywrite
3. Leomund's tiny hut, Waterbreathing (on a water adventure)
4. na
5. Rary's Telepathic Bond

Also, Tensor's floating disk on early adventures.  Often you get a ton of treasure that you can not take with you sometime before 3rd level.  After that, you get Haversacks and Bags of Holding.

I have a cleric. I have a few of the spells you list but, it's not great to keep too many niche spells slotted in my opinion. Of course, the higher you level, the more you can add.

My ritual spells are Ceremony, which I did use 1 session to prepare holy water.

Detect Magic, I've gotten more mileage out of my +6 Arcana check.

Detect Poison and Disease, I have +6 Medicine to diagnose and Lesser Restoration to cure said ailments.

Genle Repose that is always slotted as a Grave domain cleric, which I am, I have used this spell.

Silence which is situationally, very useful. Feign Death, very, very situational.

Meld into Stone, I'm not a hider/stealther, I have high AC and play support near the front lines, not a bad spell though.

Waterwalk, I have used this a few times, it's usually a planning ahead situation.

Divination, it's interesting but, not a heavy choice for 1 of my 2 level 4 spells I can cast a day.