Let me start the (hopefully long) list of answers by addressing the USA: 

 - **NSF**: (a) [Funding & Awards page][1], (b) [Funding Search (division of mathematical sciences)][2]
 - **AMS**: [AMS programs page][3], which for example leads to (a) [travel grants][4], (b) [many grants, prizes, and other opportunities][5], (c) [several fellowships][6].

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This answer is CW, feel free to edit it to include more information.


  [1]: https://beta.nsf.gov/funding
  [2]: https://beta.nsf.gov/funding/opportunities?sort_bef_combine=nsf_funding_upcoming_due_dates_DESC&f%5B0%5D=division%3A43
  [3]: http://www.ams.org/programs/programs
  [4]: http://www.ams.org/programs/travel-grants
  [5]: http://www.ams.org/opportunities
  [6]: http://www.ams.org/programs/ams-fellowships/ams-fellowships