If you need to support IE 7, definitely. But if you don't, you what? Use it anyway. The best of jQuery has been brought into the JavaScript language itself and other libraries. But jQuery still makes a lot of little things easier.
You could use the new querySelectorAll functionality in JavaScript, but learning that teaches you the basics of how to use jQuery. Also, I think jQuery still has a few selectors that aren't in querySelectorAll . Furthermore, querySelectorAll is very long to type.
You can use a different AJAX library, but is that library any easier or better than jQuery? You can do AJAX with no library, but bare JavaScript API is ugly.
It might be better to use Q for promises, but the API for Q is about the same as the jQuery promises API.
Again, you might get these things from other libraries but it has deep extend. It is much nicer to trigger events with jQuery. Ready is much nicer with jQuery.
Ironically, I'm going to refer you to http://youmightnotneedjquery.c... Because guess what? When you look, a lot of those things are a lot easier with jQuery and that site makes it clear.
Also, there are jQuery plugins. I don't think writing jQuery plugins is something that you want to do for a modern webapp, but you might find yourself supporting them.