Very easy, I do it all the time.
If you're using a form, just put the ASP variable into a hidden field and then have javascript check the value in the hidden field.
<form name="formName" id="formName">
<input type="hidden" name="varASP" id="varASP" value="<%= the.ASPvariable %>">
</form>
Then just have your Javascript read it normally:
var checkMe = document.forms['formName'].varASP.value;
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A shorter way is to just skip the form (but it's useful to mention that first because most of the times I need to check an ASP variable it's usually for a form) and reference the ASP variable directly in the javascript:
var checkMe = "<%= the.ASPvariable %>";
Note the quotes around the ASP code. That's pretty important.
Good luck!