Hay cobs - always in a treat ball, sometimes a couple from hand when bringing in from the field
Carrots and parsnips - stretches, and sometimes in haynets in winter if the grass is a little poor or they've had reduced turnout
Apples - in haynets when grazing is limited, these are rare
Very occasionally he will get some form of 'junk food' horsey treat by hand
I'm not precious and was happy at my last yard for people to give the occasional carrot. He's never been rude or nippy before, but one particular woman gave him loads and despite my saying he's had enough please stop, would continue to do so. She used to go around all the stables before going home for the evening, giving all the horses a treat or two - even with the owners gone. Funnily enough at that yard he became a little expectant and 'snuffly' and it drove me nuts
Since moving, it's stopped. He gets treats when I see fit in the way described above, and that's all.