You'll want to look into any of the street documentary greats:

  * Garry Winogrand - NYC/LA/Texas, considered by many to be the best.
  * Lee Friedlander - From Aberdeen, WA, but really shot everywhere.
  * Anthony Hernandez - Modern, still working, has moved on to larger formats of environments.
  * Joel Meyerowitz - Modern, still working, has moved on to still lifes in Tuscany, but still teaches. Pioneered a lot of early color street work.
  * Robert Frank - Released The Americans the book that really started it all.
  * Henri Cartier-Bresson - Surrealist, dream-like work that's hard to imitate.
  * Walker Evans - Worked for the Farm Services Bureau and took lots of important documentary work early in America's history.
  * Elliott Erwitt - NYC with a touch of humor.
  * Helen Levitt - NYC bad neighborhoods and life.
  * Brassai - Parisian nightlife.
  * Richard Kalvar - Still working, great work of Italy in the 70s though.
  * Leitizia Battaglia - Italian mafia in Sicily.
  * Gianni Berengo Gardin - Considered the Italian Henri Cartier-Bresson.
  * Josef Koudelka - Czech, one of the greatest documentary workers to have ever lived. Still working today and making incredible work. His book Exiles is worth everyone owning.
  * William Eggleston - Basically responsible for color photography being accepted in fine art circles.

For some contemporaries still actively shooting street I'd check out:

  * Andre Wagner https://www.instagram.com/photodre/
  * Martin Parr https://www.instagram.com/martinparrstudio/
  * Daniel Arnold https://www.instagram.com/arnold_daniel/
  * Aaron Berger https://www.instagram.com/aaronbergerfoto/
  * Alex Webb https://www.instagram.com/webb_norriswebb/
  * Matt Stuart https://www.instagram.com/mattu1/

I have dozens and dozens more if you run through those and are still interested. Street documentary work is my absolute favorite genre of photography -- got hooked after my first darkroom class at 15 -- and try to consume as much work as I can.

And no Internet post would be proper without some self promotion: https://www.instagram.com/piffeyfoto/

Edit: Ooof, formatting troubles. Never do lists on HN. Will clean up as soon as I find a README.

Edit2: Can you really not do links in a formatted list?

Edit3: Probably easiest to link to here (https://en.wikipedia.org/wiki/List_of_street_photographers) for further reference too. I realized I left so many greats and their contemporaries out just rattling off what was in my head. Nikos Economopolous, Mary Ellen Mark, Danny Lyon, Levi Levinstein and Vivian Meier -- hope they'll forgive me.