I usually take a few things, but leave the rest for the next tenants.
There is a group of about 12 guys staying in several houses. All but 1 went home for the Thanksgiving week. The 1 changed his mind and decided to go home for good. So I went to his place and he had left behind about a weeks worth of non-perishable food. I boxed it all up and am taking it to a big house where 5 of his former co-workers are staying. When they return Sunday, they'll see that the "Food Fairy" left them a box of Mexican food.
If it's non-perishable, I leave it. If it's perishable, I remove it. There are a few deviations from that policy, but not much.
You could donate to a food bank.
We discard everything except non refrigerated condiments (salt, pepper etc). We instruct our cleaners to clean everything out during each turnover.