Are there PhD programs that do not require letters of recommendation? I am applying for PhD in Mathematics. I am wondering if there are any schools or programs that do not require letters of recommendation. Do all graduate programs require these?
I've never seen a program not require a letter or recommendation when it comes to the US and I cannot speak for all other countries which can be found out by looked at other countries application process. 

If there are legitimate reasons in which you would be unable to obtain a letter of recommendation or would receive one that would not help or even hurt your chances of acceptance I would talk to an adviser who is very familiar with the application processes because sometimes they don't always spell out alternatives to certain areas of the application process when it comes to rare circumstances.