List of possible birth years of living humans

Pyke, 6 bytes

wC7m-

Try it here!

w     - 121
   m- - for i in range(^):
 C7   -  current_year-i

(After w, the codepoint for 153 is present but it isn't printable)

Pyth, 11 9 8 bytes

-L.d3C\y

Works by mapping over the range [0...120] and subtracting every number from the current year. The range is built implicitly by using 121 as the map argument. To avoid a separating whitespace between .d3 and 121 we get this number by converting y to it's codepoint.
Thanks to @FryAmTheEggman for coming up with this approach!

Try it here!

Old 9-byte solution:

_>121S.d3

Try it here!

Builds the range [1...<current year>] and only takes the last 121 elements of it.

R, 34 bytes

(format(Sys.Date(),"%Y"):0)[1:121]

See here on an online interpreter.

Edit Could be reduced to 33 bytes by using substr.

(substr(Sys.Date(),1,4):0)[1:121]

but technically this solution will only work until the 9999-12-31.