What are the essential 3.x books to own for a Pathfinder 1e GM/player?

[EisenKreutzer]

Like the title says, what are the must own books for 3.0 and/or 3.5 as a Pathfinder GM or player?

One of the things that really hooked me on Pathfinder 1e was the promise of eternal backwards compatibility with 3.x stuff.
So, now that Pathfinder 1e is no longer officially supported, what 3.x books should I look for to complete my collection?

[Psyren]

Several:

Some of the rules we use the most in our PF games are the "common item slots" from Magic Item Compendium, to discount combining commonly associated effects for slotted items. It's particularly handy in PF since there are more slots to go around, due to the mental and physical stat boosts being consolidated down to a slot apiece.

Spell Compendium is nice - even if you don't allow the spells themselves, letting toolbox spells like Limited Wish, Wish and Miracle produce effects of their level is handy.

Most if not all of the "subsystem conversions" put out by third parties, like Path of War/Grimoire of Lost Souls/Akashic Mysteries, are backwards compatible with their 3.5 inspirations. We let practitioners of those choose from both the PF and 3.5 sources freely, e.g. your Pactmaker can choose to bind 3.5 vestiges alongside Radiance House spirits. (She may have to find them first however.)

Setting books are handy if you're playing in a non-Golarion setting, especially for roleplaying info - we've run PF games set in FR and Eberron in the past, though not Greyhawk. The "monster books" are also great sources for fluff, such as Draconomicon, Libris Mortis, Lords of Madness, and the Fiendish Codices.

3.5 feats of all kinds are useful with PF's larger allotment; the Completes are usually solid sources for those.

[Silvercrys]

Depends on what you want out of them.

Players will get the most use out of the Complete books and weird subsystems like Tome of Battle, Tome of Magic, and Magic of Incarnum. Most of the Complete books only have a few gems each, though, in my opinion. Best off trying to find Tome of Magic if you have to pick just one, particularly since Magic of Incarnum and Tome of Battle have mostly been obviated by Dreamscarred Press and I've yet to find a Binder update I was happy with (though I've been out of touch with the homebrew community for close to a decade now, I pretty much dropped out of it after the WotC forums closed down and made a pretty weak attempt at connecting with it here several years ago but wasn't really into it at the time for some reason).

As far as settings go, both Eberron and the Forgotten Realms are excellent. Eberron is a lot more steampunk/magitech than (most of) Golarion, and Faerun is your bog standard high fantasy type deal with a lot of really rich lore and such if that's your speed. Should probably start with the respective Campaign Setting book to see how into it you are if you decide to do that before going whole hog on the back catalog though.

Edit: I can't believe I didn't mention Deities and Demigods and the Epic Level Handbook. Both are pretty unbalanced but they give you semi-functional rules for extending character power over very long (or rapidly progressing) campaigns, similar to the Mythic tiers in Pathfinder but as actual divinities and/or taking actual classes past level 20. Most of the rules for building characters from those books are available on the 3.5 srd at d20srd.org, I believe, if you want to check it out. I'm not sure if they have the monsters there -- they definitely don't have the example deities, but you could use the rules given to stat out the Golarion deities if you wanted.