For myself, I only allow certain things. Not including official variants (DMG) and third party variants that alter/replace rules system (e.g., spontaneous divine magic for all clerics (UA), Fewer Absolutes (Sean K Reynolds), replacing Magic Item Creation with a variant from Mystic Eye Games Artificer's Handbook, and the addition of combat maneuvers from Book of Iron Might (Malhavoc)) or DM only supplements (Green Ronin's Advanced Bestiary), player material that I allow
WOTC
PHB: Customizing a character. I am big on class variants (and, in some cases, base classes) that help create specific archetypes from both real world culture and certain fantasy books and novels provide that they fit the campaign setting and its cultures. AD&D sources that I draw ideas for 3e variants from are David Howery's revised 1e Barbarian from an issue of Dragon, Complete Fighter's Handbook kits, Complete Thief's Handbook, Complete Bard's Handbook and certain kits from Dragon Magazine.
DMG: variant spell lists and 0/0 level multiclassing at first level. The former is mandatory for clerics at first level, based upon deity and predetermined by me during campaign creation. For non-clerics, the player can talk with me and we will discuss it. As for multiclassing, the player needs to talk to me, I may have an alternate class or class variant that covers the concept or the concept may, possibly, not be viable in the campaign.
Unearthed Arcana: specific class variants and environmental race variants, certain alternate class abilities. Some things are limited to specific deities or, initially, to certain cultures based on the campaign. Such limitations are predetermined by me at campaign creation.
Cityscape web enhancement 1: The wilderness/urban skill swap.
Complete Champion: the spellless Paladin and Ranger variants
Oriental Adventures: The Shaman (slightly tweaked) replaces the PHB monk
certain feats, spells, equipment and magic items from various other books not listed from the banned WOTC books.
Banned (Not allowed at all): BoED, Magic of Incarnum, Tome of Battle, Tome of Magic, Psionics Handbook, Expanded Psionics Handbook, Complete Psionic, Races of Stone,
Third party Sources
Green Ronin:
Cavalier's Handbook (not including the class itself)
Holy Warrior's Handbook*
Psychic's Handbook**
Shaman's Handbook
Witch's Handbook
Note: the Unholy Warrior's Handbook and the Thaumaturge class (Armies of the Abyss) are in use, but DM only. Some classes are specific to certain deities or, at the start, cultures in the campaign.
*The player does tailor the abilities. the holy warrior's are prebuilt and assigned to specific deities.
** not all powers are in use.
Malhavoc
Book of Iron Might: Fighter Fighting Styles at first level.
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Monkey God/Highmoon
Equipment and material from both Frost and Fur and From Stone to Steel. What is allowable is, generally, culturally determined.
Hong's Knight: Hong's Knight variant of the OA Samurai. Knights are limited to certain cultures I allow material to be drawn from Green Ronin's Cavalier's Handbook and, for mounts, Avalanche's Noble Steeds)
Skirmisher Publishing
Experts 3.5: The Specialist class
Avalanche Press
Noble Steeds: for horses