It is most definitely 1, and that is a cool feature of how the Reals work. Think of it this way:

Try to find a number between .9999... and 1. You can't and that is why they are equal!

I had to take a proof-writing course with a pretty neat professor and he once asked me something like this for homework:

Let f(x) be the function that returns the value of the first digit after the decimal point in base 10. Is this a function? (Meaning that f(x)=f(x))
On initial inspection, I thought it was indeed a function and I wrote the proof for it. That was until I realised the morning it was due that .999... =1 and f(.99...) returns 9 and f(1) returns 0, yet the inputs are identical! Crazy shtuff, that

Standard analysis they are equal
Non-standard analysis [the hyper-reals], they are not equal

The following is an argument that makes sense to me: two real numbers are different if and only if their difference (the result of subtracting them) is not 0.  If we look at the result of subtracting .9repeating from 1, it is certainly nonnegative, but it is also less than .1, .01, .001, and so on.  So whatever this number is, if it is positive, we can find a (negative) power of 10 that is smaller than it and that it must be smaller than.  Since two numbers x and y cannot have both x>y and x<y, we have arrived at a contradiction.  Therefore, this number cannot be positive, and must be 0.