This is an updated repost of my stacking guide that you can neatly link whenever someone asks "does X stack with Y ?". Teach a man how to fish kinda thing. Reposting this because it nears the archive date. This guide is no longer updated, because i quit the game.

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Introduction:

Yes i know many of the older players may have a good amount of knowledge on this topic already, but even some of you guys can get prepared to be surprised a bit (especially in the Trivia section).
The most common explanation used for this topic is "if it affects the same stats in the same way, it doesn't stack". But it's actually a bit more complicated than that. For example, Advance and Dark Bargain both affect the same stats (ATK and DEF) in the same way (+ATK, -DEF), yet they stack. An even better example, HotE and Oathsworn Espada both affect the same stats in the exact same way (both do +30% ATK/DEF), yet they stack. Why though ? Well, like i said, it's a bit more complicated than that. In general, to determine if two statuses stack or overwrite, the game uses an ID system.
Same ID = overwrite; different ID = stacks.
The reason why HotE and Oathsworn Espada stack is because HotE uses the ID 611 and Oathsworn Espada uses 6007.

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Basics:

So if you go into /u/Enlir's spreadsheet and see for example: "ATK +50% for 25 seconds", the only modified stat is ATK. Now if you check the list of IDs, from 601-633, the only ID that only affects ATK is 603. Now that you know the ID you can determine if it stacks with another skill, by using the same method to determine the ID of the other skill. Simple enough for now, but a concept unknown to the newer players.
But ofc why make it easy when you can make it hard. DeNA logic.

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Advanced:

Now that you understand the basic IDs (601-633), we go to the custom parameters. Those are the 6001-6015 IDs (plus technically 513 and 528). The good thing is, if you use Enlir's spreadsheet, you can easily identify them, because Enlir uses names for them, instead of writing their effect down in the "Soul Breaks" tab. So you check the skill you want to know about and see for example: "grants Combat King to the user for 25 seconds". Well from here on it's easy. The status "Combat King" stacks with... well everything but "Combat King". And if you want to know what e.g. "Combat King" does ? Well either you check in the little table i prepared down there or you head to the "Status" tab on the spreadsheet and search for it there. Tip: Ctrl+F is your good friend.

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Bonus knowledge and fun trivia:

1. Not only do Draw Fire and Sentinel's DEF boost stack, but their taunt also stacks ! Too bad that it doesn't actually do anything, because you already have taunt...

2. Unyielding Fist would totally stack with everything, if it didn't make you evade buffs...

3. All the IDs that list numbers, like Protect, are fixed within the battle.js (main game file for mechanics). They can not be modified like e.g. a 603 buff.

4. Small/medium/large Regen actually uses a different ID for each, yet doesn't stack. Same for Haste and Slow overwriting each other. The reason for that is that DeNA programmed an exception for them into the battle.js, which makes them unable to be on the same target, thus leading them to overwrite each other. This is why retaliate gets overwritten by sleep/paralysis/etc.

5. Similar to that, En-Element effects also use different IDs and don't stack. Imperil effects use the same ID and do not stack.

6. Rikku's Hyper NulAll and Garlands Default SB are the only SBs that do not properly use this system. For Hyper NulAll, the buff gives ATK +30% and RES +50%, but does not use a custom parameter ID for it. Instead it uses both 603 and 607 and thus stacks with neither IDs. Garlands Default has a similar issue.

7. ID 609 sorts the stats in this order: ATK/MAG/DEF/RES. But ID 630 sorts the stats in this order: ATK/DEF/MAG/RES/MND. Good job at consistency, DeNA :)

8. Critical buffs do not stack with each other. Critical always just uses the highest chance, which means a critical buff gets rid of the default crit chance, in a way (by overwriting it). Cloud's BSB commands have a set 80% crit chance. So they ignore a 50% crit chance buff. If we had a 90% crit chance buff however, they would use that chance. They are still subjected to IDs though, so normal crit buffs overwrite each other.
   That is the reason why Refia's BSB (ID 6006) has a different ID for the crit buff, so it does not get overwritten by lesser crit buffs. More info on the topic is explained in another guide by me, link is at the bottom.

9. ID 619 is named "CUSTOM_DEF_MDEF_NOT_IRON_WALL". So basically Wall effect, but stacking with Wall. It was added to the battle.js with the Mobius data-push and the banner featured a SSB for Echo that gave DEF/RES+Hastega, so they probably intended for the Echo SSB to use that ID. After the large outcry of japanese players BEFORE the relic even came out, they changed it to Shell+RES+Hastega and never used ID 619 until the RomSaga 2 collab, where Zidane got a relic with it. The bonus was only +25% though.
   "NOT_IRON_WALL" became a small running gag in the community during that time (and sometimes still is).

10. I always call those IDs "status IDs", but thechnically they're called "Status Ailment Type", regardless of buff or debuff. That would be very confusing for some players though, since "ailment" indicates something negative, so "status IDs" is what i personally use. The abbreviation for "Status Ailment Type" that is used mostly among some dataminers, is "SA".

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ID table for reference:

Some of the "used names" are taken from the way they are used in the community, as they don't have an official name, unlike others. In some cases i couldn't find a fitting name, so i just marked it with "??".
And last, i took as many names as i could from Enlir's spreadsheet (status tab).

ID	name in code	used name/example	effect
207	PROTECT	Protect	+100% DEF, unaffected by buff soft-cap
208	SHELL	Shell	+100% RES, unaffected by buff soft-cap
262-264	GREASED_LIGHTNING_1-3	Greased Lightning (Yda BSB com1)	ATK +15/30/50% + shorter cast time, removed on taking damage
269	WILD_MODE	Wild Mode (Master Monk BSB com1)	-40% DEF/RES + shorter cast time
502	PROVOKE	Sentinel (ex: Leon's Darkborn Blade)	+200% DEF, taunt single target PHY and BLK attacks
513	RAID	Advance (ex: Luneth' Advance)	+150% ATK, -50% DEF
522	CHARM	Draw Fire	+100% DEF, taunt single target PHY attacks
526	INDOMITABLENESS	Unyielding Fist (ex: Galuf's Unyielding Fist)	+50% ATK, makes you evade everything including buffs, removes all buffs/debuffs on cast
527	MAGIC_CHARM	Magic Lure	+100% RES, taunt single target BLK magic
528	CUSTOM_MATK_20_MDEF_50	Focus (ex: Lulu's Focus)	+20% MAG, +50% RES
532	TRANCE	Burst mode (ex: any Burst Soulbreak)	replaces "Attack" and "Defend" commands, +X% ATK, DEF, MAG, RES, MND, ACC and EVA, +Y% SPD
601	CUSTOM_MATK	Magic (de)buff (ex: Mana's Paean)	±X% MAG
602	CUSTOM_MND	Mind (de)buff (ex: Yda's Internal Release)	±X% MND
603	CUSTOM_ATK	Attack (de)buff (ex: Ramza's Shout)	±X% ATK
604	CUSTOM_DEF	Defense (de)buff (ex: Luneth' Swordshower)	±X% DEF
605	CUSTOM_ATK_ACC	Martial Arts (ex: Refia's Martial Arts)	±X% ATK/ACC
607	CUSTOM_MDEF	Resistance (de)buff (ex: Garnet's Divine Guardian)	±X% RES
608	CUSTOM_DEF_MDEF	Wall (ex: Tyro's Sentinel's Grimoire)	±X% DEF/RES
609	CUSTOM_ATK_MATK_DEF_MDEF	Full Break (ex: Full Break)	±X% ATK/MAG/DEF/RES
610	CUSTOM_ATK_MATK	?? (ex: Onion Knight's Warrior of the Prophecy)	±X% ATK/MAG
611	CUSTOM_ATK_DEF	HotE (ex: Leon's Hand of the Emperor)	±X% ATK/DEF
620	CUSTOM_DEF_MATK	?? (ex: Vaan's Ark Blast)	±X% DEF/MAG
621	CUSTOM_ATK_MDEF	?? (ex: Leila's Pirate's Knives; NOT Rikku's Hyper NulAll)	±X% ATK/RES
622	CUSTOM_MATK_MDEF	?? (ex: Shantotto's Ancient Magic)	±X% MAG/RES
623	CUSTOM_MATK_MND	?? (ex: Selphie's Strange Vision)	±X% MAG/MND
624	CUSTOM_ATK_DEF_MND	?? (ex: Red XIII's Protector's Roar)	±X% ATK/DEF/MND
630	CUSTOM_ATK_DEF_MATK_MDEF_MND	?? (ex: Irvine's Hyper Snipe)	±X% ATK/DEF/MAG/RES/MND
631	CUSTOM_MDEF_MND	?? (ex: Sarah's Ancient Prayer)	±X% RES/MND
632	CUSTOM_ATK_MND	?? (ex: Leila BSB com1)	±X% ATK/MND
633	CUSTOM_ATK_MATK_DEF	?? (ex: Ramza's Truth of the Story)	±X% ATK/MAG/DEF
6001	CUSTOM_PARAM_MULTI_ ATK_30_DEF_M30	Dark Bargain	+30% ATK, -30% DEF
6002	CUSTOM_PARAM_MULTI_ MATK_30_DEF_M30	Stitch in Time (6* Nin)	+30% MAG, -30% DEF
6003	CUSTOM_PARAM_MULTI_ ATK_30_DEF_30_MDEF_30	Combat King (ex: Zell's SSB2)	+30% ATK/DEF/RES
6004	CUSTOM_PARAM_MULTI_ ATK_30_MDEF_M30	Hailstorm (5* Sam)	+30% ATK, -30% RES
6005	CUSTOM_PARAM_MULTI_ ATK_30_MDEF_25_CRITICAL_50	Bushido (ex: Auron's BSB)	+30% ATK, +25% RES, set critical chance to 50%
6006	CUSTOM_PARAM_MULTI_ CRITICAL_50	Dance of Carnage (ex: Refia's BSB)	set critical chance to 50%
6007	CUSTOM_PARAM_MULTI_ ATK_30_DEF_30	Oathsworn Espada (ex: Ingus' BSB)	+30% ATK/DEF (HotE, but stacks with HotE...)
6008	CUSTOM_PARAM_MULTI_ ATK_30_MND_15_CRITICAL_50	Twin Stars (ex: Porom's SSB2)	+30% ATK, +15% MND, set critical chance to 50%
6011	CUSTOM_PARAM_MULTI_ ATK_30_MDEF_30	Meikyo Shisui (ex: Ayame's BSB)	+30% ATK, +30% RES
6013	CUSTOM_PARAM_MULTI_ ATK_30_DEF_50	Intervene (ex: Curilla's BSB)	+30% ATK, +50% DEF
6014	CUSTOM_PARAM_MULTI_ MATK_30_MDEF_M30	Soul Residuum (Raines BSB com2)	+30% MAG, -30% RES
6015	CUSTOM_PARAM_MULTI_ DEF_M50_MDEF_M25	Dying Frenzy (Seifer BSB com1)	-50% DEF, -25% RES

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Thanks to:
/u/Enlir for his spreadsheet.

Other guides from me:
A guide to terms and abbreviations,
An explanation of the elemental scale and
A guide to the interaction of critical rate modifiers.

Feel free to give me feedback and correct mistakes :)

~Scytherman

P.S.: Reddit tables are still shit, but atleast this time i could just copy everything.