XMLHttpRequest, i.e. AJAX, without the XML.
The precise manner you do this is dependent on what JavaScript framework you're using, but if we disregard interoperability issues, your code will look something like:
var client = new XMLHttpRequest();
client.open('GET', '/foo.txt');
client.onreadystatechange = function() {
alert(client.responseText);
}
client.send();
Normally speaking, though, XMLHttpRequest isn't available on all platforms, so some fudgery is done. Once again, your best bet is to use an AJAX framework like jQuery.
One extra consideration: this will only work as long as foo.txt is on the same domain. If it's on a different domain, same-origin security policies will prevent you from reading the result.