I'm now carting around a significant quantity of jasper, tomatoes, terracotta pots, and the like. Many of these things seem insignificant, but I sometimes see items that look like they might be craftable into armor or weapons or something. Is there some reason I should not just "spam sell" all of the "vendor trash" I find around the city? I'm early in the game and could use the money, but I hate to sell something I'll need later.
These are collectively referred to as "Trade Objects." Trade objects can be sold, and their price varies depending on which type of vendor you sell them to.
Additionally, certain trade objects are required for certain quests from the vendors on Tiber Island. Finishing these quests can unlock upgrades to Ezio's equipment, which is generally going to be worth more to you than a bit of extra cash. The complete list of trade objects, along with their values and associated quests is contained in the linked wiki page.
Don't sell your loot! That was a mistake I made at the beginning of the game. Luckily I didn't sell any items that I couldn't get again (like the shrunken heads). The shop quests, only available in the shops around the main assassin fort, have items that you can only get by getting the correct items (like the best armor in the game). Additionally, the best sword in the game, altairs sword, is only available once completing all the assassin's guild objectives.
Hope this helps!