I am struggling at times with vastly too much of a specific type, such as coal in storage, during free play and missions. Is there a trash function or disposal method built in without mods that can be leveraged?
For your personal inventory, you can use logistics robot trash slots to have your logistics buddies take your excess inventory to a storage chest, but for total items in the world, there is no trash feature.
Your best bet is to plan ahead and use your circuit/logistics networks to shut off production of a given item when you have enough of it, and resume production once stocks deplete.
If your issue is too much of a given item on a specific belt loop, it helps to make sure you never have more than one kind of item per each side of a given belt. Between braiding underground belts, and using long inserters to grab from a belt an extra space away, you can manage to fit a decent variety of items through a 2 belt wide area while still keeping them organized.
For other ideas on how to control your supply flow, this Reddit thread helps https://www.reddit.com/r/factorio/comments/2vnx0u/any_alternatives_to_the_main_bus_design_concept/
And of course, check the wiki too https://wiki.factorio.com/index.php?title=Transport_belts
Here's an example of underground belt braiding http://puu.sh/9MZgq/ddfaac4791.jpg
Lastly, you can place all your unwanted items in a chest, and destroy the chest with weapons, but that would be wasteful. Don't do that!