Take a look at the $.post
function. This will send an AJAX request to your chosen URL, but unlike a regular form submission, it won't reload or change the current page.
Edit responding to comments:
You could fudge it by dynamically creating a form with a hidden input for each variable. Set the form's target to "_blank" and then submit it and that should open your other page in a new window.
$('#myLink').click(function() {
var $f = $('<form></form>')
.attr({
method : 'post',
target : '_blank',
action : 'myOtherPage.php'
})
.appendTo(document.body)
;
var myHiddenVariables = {
id : 17,
name : "Joe Bloggs"
};
for (var i in myHiddenVariables) {
$('<input type="hidden" />')
.attr({
name : i,
value : myHiddenVariables[i]
})
.appendTo($f)
;
}
$f[0].submit();
return false;
});