Does anyone know the sorts of items for whose first iteration Japanese people
have special names? The only example I can remember at the moment is for the
first leader or, to be precise, (and reveal the place I learned it), the first
Hokage, 初代. Google Translate gives me a vast number of words, all essentially
forms of "progenitor," for that particular kanji combination.

So, are there other "first" things for which Japanese people have special
names? I'm aware that the Japanese culture places special importance on the
first of anything, e.g., the first sunrise of the year, so I was hoping
someone could list the Japanese names of a few of the more famous such things.
Looking at counter dictionaries online hasn't helped me find any, and I've now
(possibly mistakenly) come to realize that these names are independent of the
counter system.
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words
What are the particular words for the first iteration of things?
The ones you're looking for usually start with
[「[初]{はつ・しょ・うい}」](http://jisho.org/words?jap=%E5%88%9D&eng=&dict=edict&tag=&sortorder=relevance)
or
[「[発]{はつ}」](http://jisho.org/words?jap=%E7%99%BA&eng=&dict=edict&tag=&sortorder=relevance).

> 初荷 はつに first cargo of the year  
>  初音 はつね first warbling heard in a New Year  
>  発刊 はっかん publish; start (new) publication  
>  発会 はっかい opening a meeting; first meeting
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I would like to add [元]{がん} to Ignacio's answer.

> 元旦 'the morning of the first day of the year'  
>  元年 'the first year of a calender system or an era'
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Just some random _very_ commonly used ones I thought of

  * 初産{ういざん} First birth
  * 初詣{はつもうで} First shrine visit of the year
  * ファーストキス First kiss
  * 初体験{はつたいけん} First experience
  * 初対面{しょたいめん} First time you meet someone
  * 初婚{しょこん} First marriage
  * 書初{かきぞ}め First calligraphy writing of the year
  * 馴{な}れ初{そ}め How you first met/got to know each other (used a lot at weddings)
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