This is the approved revision of this page, as well as being the most recent.
For seeing a person who has very unusual body features with which he was born, one can make the Bracha of Meshaneh HaBriyot. 
Going to the Zoo
For seeing a monkey or elephant for the first time one should make the Bracha of Meshaneh HaBriyot. However, if one sees another monkey or elephant, one can not make the Bracha again with Shem UMalchut, however, if it has been 30 days one can make the Bracha without Shem UMalchut. Some Sephardim hold that one can recite it with Shem Umalchut after 30 days. It’s permissible to go to the zoo to see an elephant and monkey in order to make these Bracha. 
If one sees a greater Shinui (abnormality) than the first time one can make another Bracha with Shem UMalchut. 
Even if one made a Bracha upon seeing one of the above creatures, one can still make another Bracha upon seeing another creature with a different abnormality. 
It is permitted to go to a zoo in order to see the greatest of Hashem's creations.
ShCacha Lo BeOlamo
Upon seeing a beautiful tree, creature, or person, the established Bracha was Baruch Atta Hashem…SheCacha Lo BeOlamo. However, the minhag is not to make this Bracha at all. 
S”A 225:8-9 writes that for seeing a person with a dark, albino red, or white complexion, a person who is bent over because of obesity, a midget, a person with a lot of warts, a person with hair that’s attached should make the Bracha of Meshaneh HaBriyot.
Kitzur Shulchan Aruch 60:13-14 says to say Meshaneh HaBriyot on a black person, a ginger, an albino, a midget, an extremely tall person, a retard, an amputee, a blind person, a person with boils, a monkey and an elephant.
Mishna Brurah 225:20 explains one of the above terms differently and adds the case of a person who is too tall to support his own weight.
Piskei Teshuvot 225:20 in name of Sh”t Shevut Yacov 1:4 writes that the case of Siamese twins is a reason for this Bracha.
The Chaye Adam (Vol 1, chapter 63:1) writes that our minhag is not to make the Bracha on seeing a person of dark complexion or a midget since we see these are common sight for us.
Orchot Rabbenu (Vol 1 pg 94) writes that the Steipler made a Bracha on seeing a midget.
Piskei Teshuvot 225:20 concludes that the Bracha should only be made for seeing a person who has a very significant change.
↑ The Mishna Brurah 225:30 writes practically after 30 days one should only recite the bracha without Shem Umalchut. Vezot HaBracha (pg 156), Piskei Teshuvot 225:21, Kesot HaShulchan 66:8, Halacha Brurah (Siman 225:56; Rav Dovid Yosef), and Birkat Hashem (vol 4, pg 249; Rav Moshe HaLevi) all agree and hold like the simple explanation of S”A that there’s no Bracha on the elephant or monkey every thirty days but only the first time. Birkat Hashem adds that even if one didn’t make the Bracha the first time one can’t make it the second time. [This is in accordance with Biur Halacha 218:1 s.v. BeMakom.] However, Yalkut Yosef (5751, 225:21, vol 3 pg 609) writes that the minhag is to make the Bracha on the elephant and monkey every thirty days.
↑ Orchot Rabbenu (vol 1 pg 94) writes that the Steipler took his children to the zoo to make this Bracha. This is also the opinion of the Yalkut Yosef (vol 3 pg 608).
↑Yalkut Yosef 223-225:21 writes that there's no prohibition to go to a zoo because of a concern of Al Tifnu El Mdatchem, pursuing vane sights. hidabroot.org quotes Yeshuot Chachma 33:11 that looking at non-kosher animals brings a negative spiritual force upon a person.
↑ Chaye Adam (Vol 1 63:1) writes that the minhag is not to make this Bracha since it’s common for us to see beautiful sights. Mishna Brurah 225:32 agrees and in Shaar HaTziyun he adds another reason; since the Bracha was only established for a very beautiful sight and no one is able to properly distinguish which sights are exceptionally beautiful. The Artscroll Siddur writes that many make this Bracha without Shem UMalchut.