In Diablo 2 (I believe they came in LoD) there were Charms. Items that gave you buffs by just having them in your inventory. Is there anything even close to this system in Diablo 3, or is it only your gear and passives that give you stats.
There are no items similar to D2's charms in Diablo III. The only items that are really worth keeping in the inventory as you adventure are potion stacks.
In earlier iterations of Diablo III's design there used to be a charm-like system called "talisman" that did not occupy inventory space, see on the left here:
But it was removed after Blizzard were not happy with how it worked. There were vague hints by Blizzard that it might return, but at the moment it's not a confirmed future feature.
Unfortunately there is nothing like charms in D3. Perhaps they will look to add something similar in the future.
Currently it is only your gear and passive skills that give you stats.
You can also get some bonuses from equipping your follower with certain gear (i.e. magic find, gold find, etc...).
No, Diablo 3 does not currently have any items which give you benefits just by having them in your inventory. As you said, these were added to Diablo 2 after its release, so they may come to Diablo 3 at some time, but I think the designers have said that they weren't too happy with the way they worked.