This can be refined using a loop to eg. not focus certain types of field, disabled fields and so on. Better may be to add a class="autofocus" to the field you actually do want focused, and loop over forms[i].elements[j] looking for that className.
Anyhow: it's not normally a good idea to do this on every page. When you focus an input the user loses the ability to eg. scroll the page from the keyboard. If unexpected, this can be annoying, so only auto-focus when you're pretty sure that using the form field is going to be what the user wants to do. ie. if you're Google.
Putting this code at the end of your body tag will focus the first visible, non-hidden enabled element on the screen automatically. It will handle most cases I can come up with on short notice.
Although this doesn't answer the question (requiring a common script), I though it might be useful for others to know that HTML5 introduces the 'autofocus' attribute:
This gets the first of any visible common input, including textareas and select boxes. This also makes sure they aren't hidden, disabled or readonly. it also allows for a target div, which I use in my software (ie, first input inside of this form).
I needed to solve this problem for a form that is being displayed dynamically in a modal div on my page, and unfortunately autofocus isn't honored when the containing div is shown by changing the display property (at least not in Chrome). I don't like any of the solutions that require my code to infer which control I should set the focus to, because of the complications of hidden or zero-sized inputs, etc. My solution was to set the autofocus attribute on my input anyway, then set the focus in my code when I show the div: