I would say that JS does support associative arrays, since it is the fundamental data type behind objects and arrays. Arrays are basically associative arrays, since the index is converted into a string and used as a key.
E.g. myData is equivalent to myData["7"].
The length property does not return the number of items in the array though. It returns the value of the key with the highest numerical value if parsed as a integer plus one.
>>> Moreover building a hash over an Array object is potentially dangerous. If anyone extends Array.prototype with enumerable properties (as, for example, the Prototype.js library does) these will be read in during for…in iterations, wreaking havoc with your logic (or at least requiring you to make use of the clunky hasOwnProperty method). Build hashes over Object and nothing else, since by convention Object.prototype is not augmented.
This is a gotcha in Lua, too, but there it makes a bit more sense - tables ("dicts", if you prefer) explicitly have a key/value part and an array part - if you have a table with keys 1* to N, it's handled internally as an array (with O(1) lookups), but #, the length operator, explicitly gives you the upper bound for the array portion. In practice, this isn't a big deal, since the very different performance etc. means that they're usually used in very different ways.
* Yeah, Lua is 1-indexed. Nothing's perfect. Lisp has all those parens, Python has the whitespace thing...you get over it. :)