I own all the books on here already, but as I was buying Tasha's, I thought about this. The core books are of course good, but what would y'all recommend? 

I mean, there really isn’t much difference?  I think the table as a whole should own the PHB, DMG, Monster Manual, Xanathar, and now Tashas.    Those are the big ones now.  Even players can get plenty of use out of the DMG. Volos if you want more monsters, but Players shouldn’t be in the Monster Manual or Volos.  The rest are just settings, but in terms of essentials?  Those five.  

"What books are essential for a player or DM?"

None. The only thing that is essential is the Basic Rules and SRD which are free by using the Basic Rules link in the Sources menu or downloading the PDFs from Wizards of the Coast's website.

Everything else is extra fluffiness.

Good optional fluffiness would be the core 3: PHB, MM and DMG, and I would recommend XGtEfor all the fluffies it offers for both players and DMs. It has extra character options, spiffy tables for generating backstories and character ideas, extra clarity on conditional/situational rules plus alternative rules. It's just good nutritious moreness.

Beyond that, there's the books that offer more options for players like SCAG or E:RotLW (even if you don't play in Eberron, there's a lot you could basically copy over into your own campaign).

Being the Critical Role fanthing that I am, I also recommend EGtW. Even if you don't want to play in Exandria, the book serves as a brilliant campaign guide that you can emulate for your own campaigns and take inspiration on how to tackle campaign-immersive characters effortlessly. So for a DM  it is a great example if you want to consider your own version for your own homebrewed world. It's genuinely one of the better campaign guides out there, IMHO, if RP and immersion are your thing. Definitely one for DMs to get their teeth into (another food reference, am I hungry?).

Good gravy (another one? where's the fridge) there's a lot of acronyms in D&D. Go figure.

Addendum: As for Tasha's, I shall withold judgement until my tasting when it is cooked and served. Now, on to the Sammich Station!

The only published material that can truly be considered “essential” are the free Basic Rules & SRD, which DDB has conveniently compiled together for us available right here for free: https://www.dndbeyond.com/sources/basic-rules

But that is just the absolutely bare minimum required materials to actually make characters and run a game. The Player’s Handbook, the Dungeon Master’s Guide, and the Monster Manual contain all of that, and everything else to play the full game. Those three are officially referred to as the three “Core Rulebooks.”

Xanathar’s Guide to Everything entirely optional, but it is so useful, and so popular that many people just consider it “the unofficial 4th Core Book.”

Everything else will generally get you mixed reactions depending on who you ask about them.

The new book coming out in less than two weeks, Tasha’s Cauldron of Everything, will either be the absolute best thing to happen to 5e, the absolute worst, or half each. It really does seem to be that divisive.

English to [Language] Dictionary

As a player, the books I go to most often are the PHB, MM, and XGE. As a DM I also use the DMG, Volo's, and MTF (albeit, I use the last two far less), plus an adventure guide if I happen to be using one. I own the sourcebooks but I don't really use them that much.

One book that I really like as a DM is The Monsters Know What They're Doing by Keith Ammann (he also has a blog by the same name). He analyzes the stats and psychology of monsters and suggests tactics and SOPs for them that I find very useful. I'm a big tactics guy, so I don't like it when combat is just a drawn-out slugfest. It's not fun for me as a player or DM. He also has a companion book for players, Live to Tell the Tale, but I could really take or leave it. It has a few good pointers, but nothing stellar. 

Players at my table use the MM a lot specifically for Polymorph, although I do agree that players having it at the table is often problematic. 

Quote from Weezard >>

Players at my table use the MM a lot specifically for Polymorph, although I do agree that players having it at the table is often problematic. 

 In the Online Age, there is no practical way for me to stop them from looking things up while we play. If they are fighting a Hydra, one of them, or heck all of them, could theoretically have their 2nd monitor up or their iPhone up with the MM stat block for the Hydra, and heck even keeping track on pencil and paper (or a notepad file) of how many HP it has. I trust them not to do this, but they potentially could do so.

However, at the table, I would never allow them to look at MM. Polymorph is one spell... you don't get to have all this metagame knowledge right there at the table in case you wanna cast one spell.

Also, I question whether even for the purpose of that spell it is necessary to know the exact stat block. Unless the character is some sort of naturalist (a Beast Master with a high Nature skill or something) it is unreasonable for them to claim they know enough about the creatures into which they might polymorph that they would ICly know the stat-based differences between, say, a Giant Eagle and a Grizzly Bear, other than the simply obvious (claws vs talons, flight vs hibernation, etc.)

Quote from Weezard >>

One book that I really like as a DM is The Monsters Know What They're Doing by Keith Ammann (he also has a blog by the same name). He analyzes the stats and psychology of monsters and suggests tactics and SOPs for them that I find very useful. I'm a big tactics guy, so I don't like it when combat is just a drawn-out slugfest. It's not fun for me as a player or DM. He also has a companion book for players, Live to Tell the Tale, but I could really take or leave it. It has a few good pointers, but nothing stellar. 

 That book is one of my favorites. The book itself contains all the monsters from the DMG, and is extremely useful. I'd recommend it for any DM who plans to do more than 2 or 3 sessions. The blog has tactics for a bunch of creatures in other books, such as VGtM and MToF. 

Thanks for all the feedback everyone! I currently have physical copies of the PHB, DMG, MM, VGtM, MToF, XGtE, and EGtW, as well as the third party Tal'Dorei Campaign guide, as I'm a critter as well. Was thinking about adding Theros, Ravnica, and Eberron for game inspiration for when I run in person again after the plague as a handy reference without the temptation of getting sidetracked. I actually own the Keith Ammann audiobook and am about halfway through, but wish I would have also bought a copy of the book or ebook to make referencing it easier in practical application. 

If you already know how to play, then the only book one needs is the Players Handbook. The adversaries can all be humanoid NPCs. Also, the Players Handbook stats common Beasts.

Because they supply player options, Xanathars and Tashas are also useful.

The DMs Guide has good advice, and can inspire DM creativity. (Unfortunately, some important skill information that should be in the Players Handbook is in the DMs Guide.) And the DMs Guide has magic items. But again, if one already knows how to play, it is easy for a DM to create ones own magic items, even using Players Handbook spells for inspiration. The Monster Manual is useful for "monster of the week" flavor, or a generally exotic world filled with weird creatures. Similarly, Volos expands weird creatures, and Mordenkeinans expands exotic worlds.

Personally, I am a fan of urban settings, and love Eberron and Ravnica, mixing both.

For myself, as a player AND DM, I'd say that the number one MOST IMPORTANT book of all, is the Player's Handbook. You have all the basic resources you need as a player, including rules on dice, references for conditions (surprised, when to roll advantage, falling damage calculator, ect.), and the entire character creation toolbox. Plus, the all-important, not found in any other book, SPELL LIST. Even in my own Discord-chat D&D groups, we'll have someone decide "I'll cast 'Identify'...do I roll for that?" and with the Player's Handbook on my desk, sometimes I can find the spell faster than the other players can digitally share it, so it's still relevant. And as a DM, you can homebrew a lot off of the info in the PH. 

The next most important book may actually be the Dungeon Master's Guide. The Monster Manual does compete for second most important, but it comes down to this: are you the kind of DM who wants more material plane interactive encounters that are made mostly of monsters and NPC's, or do you want to explore deeper into the creation of your world with advanced information on the planes of the multiverse, new character creation rules, magic items, and town/village creation tables? For me, the DM's Guide has been the most helpful; the Monster Manual shouldn't, however, be underappreciated. 

Having borrowed Xanathar's Guide to Everything from the library a year ago, and surviving this far without it, I'd say it's a great book but not *completely essential* to DM's like the two above mentioned guide. However, it'd be a great addition to any collection! 

I am going to purchase Tasha's Cauldron of Everything because I've heard it has more expanded information on magic (ooooh! yeeeaaaah!!!!), as well as some revisions considering the concept of race/ancestry in relation to character creation. Even if all this information will be available digitally in time, there really is nothing like turning paper pages in a book with the screens turned off; the information sinks into my own memory deeper when I read this way, and it's good for the mind and eyes to have screen breaks.