Destiny

Destiny was philosophico-religious concept about what will and must happen that not all agreed with. Peri Brown thought that destiny was "just a fancy name for blind chance", while Yrcanos said that, if that were true, life would be meaningless. (TV: Mindwarp)

Destiny was something that must not be messed with. Amy Pond asked her younger self, "You're asking me to defy destiny, causality, the nexus of time itself, for a boy?" The Eleventh Doctor thought it impossible to "defeat pre-destiny", which he did manage to do. (TV: The Girl Who Waited) While something may have been erased from destiny, its possibility was still imprinted on the structure of the universe. (PROSE: Falls the Shadow)

When Donna Noble parked her car right next to where the Tenth Doctor would park his TARDIS, she said, "This is like destiny!" (TV: Partners in Crime) The Meta-Crisis Tenth Doctor later confirmed this:

It's like we were always heading for this. You came to the TARDIS. And you found me again. Your granddad. Your car. Donna, your car. You parked your car right where the TARDIS was going to land. That's not coincidence at all! We've been blind. Something's been drawing us together for such a long time.Meta-Crisis Tenth Doctor

"Destiny", or rather Dalek Caan's manipulation of time, lead the Doctor to meet Donna twice, and her grandfather, so that Donna could become the Doctor-Donna and the Meta-Crisis Doctor could be created. This became instrumental in the defeat of Davros's plan to destroy all universes through the reality bomb. (TV: Journey's End)

After the Eleventh Doctor lost Clara Oswald again in Victorian London on Christmas 1892, he began searching for another version of her, hoping that, if he just wandered around enough, he'd find her eventually, "like destiny, sort of". A young Clara Oswald, who the Doctor did not recognise, called destiny "rubbish". (WC: The Bells of Saint John: A Prequel)

References

The Sixth Doctor said that "an advanced culture manipulating the destinies of a less developed civilisation" must be stopped; the Valeyard called these words arrogant in a Zenobia court. (TV: Mindwarp) Earlier in his time, Davros asked the Fourth Doctor if he thought he could change the course of destiny, to which the Doctor replied "let's just say I might tamper with it." (TV: Destiny of the Daleks)

The Black Guardian claimed to control the Fifth Doctor's destiny. (TV: Enlightenment)

When one began to reach their goals, such as De Flores coming close to forming the Fourth Reich, they felt that their destiny was approaching. In traveling to 1988 Lady Peinforte said that "destiny beckons." (TV: Silver Nemesis)