Out with the Old

Once you reach a certain level, unless you're living in a very remote location, at some point your items bag will become full.
You can remedy this by throwing away some of your less valuable items. Specifically, potions (not the super potions or the hyper potions, but the standard potions) and revives can generally be tossed in large quantities
Keeping a small stash of revives and potions will leave plenty of room for the more essential pokeballs.
Once you start getting super and hyper potions regularly, standard potions can be tossed completely!

You'll generally have way more revives and standard potions than you need.