Better Than Canon
Most fans just aren't content to accept absolutely everything the canon offers. In fact, visit any forum and you'll find a lot more complaints about pretty much every aspect of the canon than compliments. In some cases, this may be warranted. But what can one actually do about these things? Simple: just exercise some "creative re-interpretation".
No examples, please; we'd be here all day. This is an Omnipresent Trope.
- Alternate Character Interpretation
- Alternate Universe Fic
- Creator's Pet (same as The Scrappy)
- Dark Fic
- Elsewhere Fic
- Fan Fiction (a good chunk of it in general)
- Fan-Preferred Couple
- Crack Pairing (what the above can lead to)
- Fanon Discontinuity
- Fix Fic
- Patchwork Fic (using characterization or elements from Alternate Continuity to tweak "mainline" continuity)
- Possession Sue (rewriting a canon character to fit the author's ideals and/or tastes)
- The Scrappy (desire to kill or otherwise just remove the character)
- Slash Fic (when the characters are straight in canon, at least)
Some of the works on the Fan Fic Recommendations pages might be this.