Why do some Sharingan eyes have unique Mangekyou abilities? Itachi, Sasuke, Madara's Sharingan and Danzo's "Sharingan" eyes have the "standard" Mangekyou abilities of Amaterasu, Tsukuyomi, Susanoo, Izanagi and Izanami. (Granted not all of them have used all the abilities.)  

However, Shisui and Obito's sharingan have unique Mangekyou abilities (Komoamatsukami and Kamui respectively). Why do some Sharingan eyes come with unique abilities? Do they get these abilities in lieu of the standard abilities or in addition to them?  

Obito has always used Kamui and never been shown using the standard abilities, with his Sharingan (he once used Izanagi with a transplanted Sharingan), which makes me wonder if the special abilities are in lieu of the standard ones.
Each Mangekyo is given a different eye pattern, and a different ability. Mangekyo literally translates to kaleidoscope, where each time you look you see a different, symmetric shape. 


Itachi had access to Amaterasu and Tsukuyomi
Sasuke used Amaterasu and Kagutsuchi, which allowed him to shape and control his Amaterasu
Obito has Kamui. Obito also uses "throw-away" Sharingan eyes for Izanagi.
Shisui has a different one, the Kotoamatsukami.
Madara's ,Izuna's, and Indra's eye techniques were not revealed. 
Kakashi has Kamui as well, since it's technically Obito's eye.
Danzo can use Shisui's Kotoamatsukami, since he has his eye. It's unknown if he can also any other Mangekyo Sharingan abilities with it (like Amaterasu or Tsukuyomi).


Also


Susano'o is achieved once you control both of the techniques in your eyes, regardless of what they are. That's the reason Kakashi (And Obito) for instance cannot ever achieve a Susano'o individually, but could when 



   Obito's spirit possessed Kakashi and gave him both Mangekyo Sharingan


Which technique you gain isn't "predetermined". You cannot discern it before you gain the Mangekyo and it seems to be random, however it may be linked to an individual's personality and skill set - Itachi was incredibly skilled with Genjutsu, and gained the Tsukuyomi. Sasuke was shown to be very skilled with Fire Release jutsu and for much of the anime had a burning hatred inside of him, which may be why he gained incredible control over his Amaterasu. This is pure speculation however.

Many people have been speculating that Madara had to have the Tsukuyomi due to his use of Genjutsu on Oonoki, however all Sharingan users, whether or not they have the Mangekyo, can cast Genjutsu simply via eye-contact. The strength of this varies with the strength of the user, but with how powerful Madara is, his Genjutsu: Sharingan approaching Tsukuyomi levels of strength would not be unreasonable. 

Additionally, Izanagi and Izanami are both jutsu that can be used by simple Sharingan users, without need of a Mangekyo or Senju DNA.

Ref: http://naruto.wikia.com/wiki/Sharingan , http://naruto.wikia.com/wiki/Mangeky%C5%8D_Sharingan