These aren't mine (I've yet to start a Gundam fanfiction) but they're worth reading. These are all Gundam SEED/Destiny fics, but I think anyone who reads them can appreciate them:
Respect Between Enemies - By TheBetanWerecat. Takes place at The Descending Sword and progresses to the beginning of the two-year ceasefire. Mainly original characters with guest characters from the show, with its own separate plot helped along by the main plot.
Second Chance,
The Necklace,
Gundam SEED: Evolutions - By Enchanter468. Three stories with an ongoing plot. This is a KiraxFlay-centric set of story, in which Flay survives the final battle at Jachin Due.
Fallen Angel - By NoshMono. Main story takes place at Episode 23: The Shadows of War in Gundam SEED Destiny, and quickly and radically changes the plot, into something much, much better than Destiny. This is a KiraxFlay-centric story. You will be very much surprised at who lives and who dies in this fanfiction. This story has also been completed.
Soaring Above - By NoshMono, and sequel to Fallen Angel. Takes place between the end of Fallen Angel and its epilogue; will naturally have its own, completely original plot. This is a Shinn-centric story (I don't want to spoil who he's been paired up with). Kira will
not steal the spotlight in this story, even though he does have a role in it.