All browsers except IE6-8/Opera

Set HTMLInputElement.setSelectionRange() to the length of the input value after explicitly setting the focus(). The disadvantage is that it scrolls back to start once blurred.

var foo = document.getElementById(foo);

foo.value = http://stackoverflow.com/questions/1962168/scroll-to-the-very-right-of-a-long-text-input;

foo.focus();

foo.setSelectionRange(foo.value.length,foo.value.length);

<input id=foo>  

All browsers except IE/Opera

If you don't care about IE in its entirety, then set Element.scrollLeft to Element.scrollWidth. The disadvantage is the less browser support.

var foo = document.getElementById(foo);

foo.value = http://stackoverflow.com/questions/1962168/scroll-to-the-very-right-of-a-long-text-input;

foo.scrollLeft = foo.scrollWidth;

<input id=foo>

All browsers

If you'd like to support every single browser, consider to trick it with the dir (direction) attribute which you set to rtl (right-to-left). The disadvantage is that it's a hack which really need to be taken into consideration when it's editable and/or you develop a direction sensitive website, but this works on all browsers and is great on readonly inputs.

var foo = document.getElementById(foo);

foo.value = http://stackoverflow.com/questions/1962168/scroll-to-the-very-right-of-a-long-text-input;

<input id=foo dir=rtl>