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?
While you can not delete items directly, you can place them inside a container and destroy this container by using your weapon (press 'c' to hit highlighted target) or ramming it with a vehicle.
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!
1upvoted for the braiding link Feb 29, 2016 at 18:15
1There is also a trash mod, though now I can't find it... Mar 21, 2016 at 7:06
there is now a mod (in the interest of full disclosure I wrote it)