I use JQuery in a classic ASP website.
It works very well. Where needed I can put some ASP stuff into javascript blocks to use stuff from database:
function myjavascripfunction(){
$("#pageTitle").html(<%= rs("Title")%>);
}
Using JQuery with ASP is great if you are unskilled in classic ASP and don't want to waste too much time on it.
PS:
There's a ASP-to-JSON library that allows you to convert DB queries into JSON objects. Great for making .html pages that do ajax calls on .asp pages who's only job is to retrieve some stuff from the DB.
This way you have a reuseable .html page that you can just copy paste when you switch to another serverside language. All you'd need to do is make some .php or .aspx pages that also return JSON and call those instead of the .asp ones.