Calculate the day number of the year

JavaScript ES6, 81 69 bytes

(y,m,d)=>d+parseInt("03479cehkmpr"[--m],36)+m*28-(y%(y%25?4:16)&&m>1)

Assuming months are 1-based, otherwise I could save 2 bytes.

Edit: Saved 12 bytes using @user81655's tip.

C, 96 102 89 61 bytes

g(y,m,d){printf("%d",m/2*31+--m/2*30-(y%(y%25?4:16)?2:1)+d);}

Pyth, 31 bytes

+s<X1+L28jC"3Ȕ"4!%|F_jQ*TT4tEE

Thanks to @Dennis and @Jakube for the leap year portion. Input is YYYY, MM, DD on separate lines.

+                          add [day] to
  s <                      sum of first [month]-1 values in the list
      X                    add 1 to
        1                  the second element (January)...
        +L                 \
           28              |
           j               }   lengths of all the months
             C "3Ȕ"       | 
             4             /
        ! %                ... if the year is a leap year; that is, 4 divides...
            |F _ j         fold logical OR over reversed
                   Q       the year
                   *TT     converted to base 100
            4
      t E                 [month]-1
  E                       [day]

Test suite.