Most of that awesome looking armor comes from dungeons. The one you have pictured there is the Foestriker's set. That one in particular is available from the first three dungeons(Sastasha, Tam-Tara Deepcroft, Copperbell Mines) alongside the Acolyte's set.
Foestriker & Acolyte's set
http://img.finalfantasyxiv.com/lds/p...jpg?1383198528http://img.finalfantasyxiv.com/lds/p...jpg?1383198528
The next three sets of unique looking armor sets comes from Brayflox's Longstop.
Cavalry, Infantry & Battlemage sets
http://img.finalfantasyxiv.com/lds/p...jpg?1383198528http://img.finalfantasyxiv.com/lds/p...jpg?1383198528http://img.finalfantasyxiv.com/lds/p...jpg?1383198528
The rest that are shown are crafted.
Vanya robe & Gryphonskin sets
http://img.finalfantasyxiv.com/lds/p...jpg?1383198528http://img.finalfantasyxiv.com/lds/p...jpg?1383198528
And this is the Tin-can armor we all hate. In this image, Akihiko Yoshida drew it without the helmet.
http://img.finalfantasyxiv.com/lds/p...jpg?1383198528
