How to compare variables to undefined, if I don’t know whether they exist?

The best way is to check the type, because undefined/null/false are a tricky thing in JS. So:

if(typeof obj !== "undefined") {
    // obj is a valid variable, do something here.
}

Note that typeof always returns a string, and doesn't generate an error if the variable doesn't exist at all.

if (obj === undefined)
{
    // Create obj
}

If you are doing extensive javascript programming you should get in the habit of using === and !== when you want to make a type specific check.

Also if you are going to be doing a fair amount of javascript, I suggest running code through JSLint http://www.jslint.com it might seem a bit draconian at first, but most of the things JSLint warns you about will eventually come back to bite you.

if (document.getElementById('theElement')) // do whatever after this

For undefined things that throw errors, test the property name of the parent object instead of just the variable name - so instead of:

if (blah) ...

do:

if (window.blah) ...