From the spec, §15.9.1.1:

A Date object contains a Number indicating a particular instant in time to within a millisecond. Such a Number is called a time value. A time value may also be NaN, indicating that the Date object does not represent a specific instant of time.

Time is measured in ECMAScript in milliseconds since 01 January, 1970 UTC. In time values leap seconds are ignored. It is assumed that there are exactly 86,400,000 milliseconds per day. ECMAScript Number values can represent all integers from –9,007,199,254,740,992 to 9,007,199,254,740,992; this range suffices to measure times to millisecond precision for any instant that is within approximately 285,616 years, either forward or backward, from 01 January, 1970 UTC.

The actual range of times supported by ECMAScript Date objects is slightly smaller: exactly –100,000,000 days to 100,000,000 days measured relative to midnight at the beginning of 01 January, 1970 UTC. This gives a range of 8,640,000,000,000,000 milliseconds to either side of 01 January, 1970 UTC.

The exact moment of midnight at the beginning of 01 January, 1970 UTC is represented by the value +0.

The third paragraph being the most relevant. Based on that paragraph, we can get the precise earliest date per spec from new Date(-8640000000000000), which is Tuesday, April 20th, 271,821 BCE (BCE = Before Common Era, e.g., the year -271,821).

Date does not have this

Actually, it does, but only indirectly. According to the specification, a Date object's milliseconds-since-the-Epoch value can only be in the range -8640000000000000 to 8640000000000000.

So the minimum date is new Date(-8640000000000000) (Tue, 20 Apr -271821 00:00:00 GMT), and the maximum date is new Date(8640000000000000) (Sat, 13 Sep 275760 00:00:00 GMT).

If you wanted, you could put those on the Date function as properties:

Date.MIN_VALUE = new Date(-8640000000000000);
Date.MAX_VALUE = new Date(8640000000000000);

...but since Date instances are mutable, I probably wouldn't, because it's too easy to accidentally modify one of them. An alternative would be to do this:

Object.defineProperties(Date, {
    MIN_VALUE: {
      value: -8640000000000000 // A number, not a date
    },
    MAX_VALUE: {
      value: 8640000000000000
    }
});

That defines properties on Date that cannot be changed that have the min/max numeric value for dates. (On a JavaScript engine that has ES5 support.)

When a string passed into a Date constructor is not in extended ISO format the parsing is completely implementation dependant. If it is in ISO format the parsing is well-defined and it will work exactly the way you want:

var myDate = new Date('0001-01-01T00:00:00Z');
console.log( myDate.getUTCFullYear() );