Cacti have always been farmable completely automatically. With pistons in 1.7, sugar cane can now be farmed in a fully automatic fashion as well. Mobs and animals can be farmed as well in giant mob grinders. To my knowledge these are the only items that can be farmed in a fully automatic fashion in vanilla Minecraft.
Cobblestone can be farmed fully automatically using mods, or in a semi-automatic fashion using TNT. Wheat can be farmed semi-automatically on a massive scale, but unfortunately requires replanting and tilling.
What I'd like to know is if there are any contraptions people have contrived to harvest any other item in a fully automatic way without using any mods.
Best Answer
Aside from the things you mentioned:
Fully Automatic (no need for player's presence):
As long as you keep the chunk loaded, you can go on an adventure while your farm is producing
Fully Automatic, as long as player is within 128 blocks of farm
AFK farms:
You may need to jam the click button, and you wont be able to play while harvesting