Can you counter your own spell to prevent it from resolving?

There is no rule in Magic that prevents a player from targeting their own spells or permanents with effects, including counterspells. CR 114.1 establishes that targets are chosen by the controller of the spell or ability, and nothing restricts that target from being something you yourself control. If you control a counterspell like Cancel, you may legally target your own spell on the stack.

When the counterspell resolves, your spell is countered and placed into your graveyard without resolving (CR 701.5a). This can be strategically useful — for example, to trigger a 'whenever a spell you control is countered' ability, to put a card into your graveyard for graveyard-matters strategies, or to prevent an opponent from copying or otherwise interacting with the spell before it resolves.

Priority rules (CR 117.3) mean that after you cast a spell, your opponent gets priority first, but you will eventually have the opportunity to respond to your own spell by casting a counterspell during that same stack window, as long as you have priority.

Concrete example: You cast Divination, then realize your opponent has a Reverberate ready to copy it. You respond by casting Counterspell targeting your own Divination. Counterspell resolves first, countering Divination — now your opponent has nothing to copy with Reverberate.

Note that some countering effects are mandatory (e.g., 'counter target spell') but the same principle applies — you simply choose your own spell as the legal target (CR 114.1, 701.5a).