Short answer: +/- 9007199254740991
According to the ES6 specification, all the positive and negative integers whose magnitude is no greater than 2^53 are representable in the Number type (indeed, the integer 0 has two representations, +0 and −0). In ES6, this is defined as Number.MAX_SAFE_INTEGER.
Note that the bitwise operators and shift operators operate on 32-bit ints, so in that case, the max safe integer is 2^31-1, or 2147483647.