I first point out that for the most part, all the prior answers are correct. Yes, all gold passives do stack, however, there's a bit of a catch. As of Patch 3.14 the gold granting items were overhauled. With the exception of Avarice Blade, a character is not allowed to posses more than one "Gold Income" item. The Gold Income items are:
- Jungle Items
- Spirit of the Spectral Wraith - Conservation
- Spirit of the Lizard Elder - Conservation
- Spirit of the Ancient Golem - Conservation
- Wriggle's Lantern - 40% More gold from jungle monsters
- Support items
- Relic Shield / Targon's Brace / Face of the Mountain - Spoils of War
- Ancient Coin / Nomad's Medallion / Talisman of Ascension - Favor
- Spelltheif's Edge / Frostfang / Frost Queen's Claim - Tribute
Keep in mind the support items do change the passives a little with each upgrade, as well as two of them including a gold per 10 seconds. In theory, the passives from these items would indeed stack, but the game does not allow you to have more than one.
Any other Gold related passives, such as Twisted Fate's passive ability (keep in mind it is no longer a team-wide effect), Draven's passive, and Ashe's Hawkshot
E passive, will stack with Avarice Blade, and effects of the gold income items.