What are Byakuya's Gokei, Senkei and Shuukei? In addition to his bankai, Byakuya is observed using three techniques:


Gokei


   I think it was in battle with Hitsugaya's Reigai, though I'm not sure

Senkei


   while fighting Ichigo at Rukia's execution

Shūkei


   in the same fight as above



Not only is this the largest number of Zanpakutō abilities that we have seen in one sword (I think), but each one of them seems more powerful than the last (and more powerful than his bankai!).

So what exactly are those three techniques? Why is Byakuya the only one in Bleach to have so many different techniques contained in his Zanpakutō?
They are various forms of his bankai, achieved by arranging the blades in different patterns. His bankai is versatile by nature (being composed of countless tiny blade fragments), and affords him several forms, with varying combination of attack and defense. 

Whether a bankai can have multiple forms depends on its nature. Hitsugaya Toshiro and Abarai Renji could also achieve multiple bankai forms with practice/training. The former could mold Hyorinmaru's ice into various forms (like fairy-tail's Gray), while the latter could rearrange Zabimaru's segments. Shinigami such as Komamura, Tousen, or Soifon would likely not have multiple bankai forms due to the nature of their bankai.

By the way, Byakuya is no longer the only known shinigami with multiple bankai forms


   as Yamamoto Shigekuni's bankai has been revealed.


Also, Byakuya's sister, Rukia, has shikai with multiple forms:


   Tsukishiro, Hakuren, Shirafune, and Juhaku