When to use jQuery?

If a web page only requires very simple functionality (like form validation) then you might consider writing pure javascript. It will make your web pages more efficient since it doesn't have to download a giant jQuery file. The caveat to this is that browsers very often do not interpret javascript the same, or their DOMs may be implemented differently. This is less of an issue in recent versions of major browsers, but if you're writing scripts for older browsers then it is probably advisable that you just use jQuery. (This is really the big reason jQuery was created to begin with).

jQuery solves cross-browser issues, has lots of nice plugins you can use and just has a better interface than native javascript and the DOM. However, if you're using jQuery for one small feature of your website, then you're effectively bringing in a bunch of code you're not using. If your webpage doesn't use ajax, then you're not going to use the $.ajax() method. But it is still there and it is taking up space causing your web page to load just a little more slowly. The same goes for ALL of the other jQuery code you're not using.

I think it just really boils down to your goals. If you just want to create a quick and easy project, support older browsers or have some really heavy javascript based effects then I think your best bet is to use jQuery. If you decide that you are going to use jQuery for anything, then you should probably use jQuery for everything. I wouldn't import jQuery for animations and then use vanilla javascript for form validations.

If you're worried a lot about efficiency I would consider using pure javascript (perhaps look into some javascript micro-libraries.) If you do decide to write in pure javascript, then you should do your research on writing cross-browser javascript and have a good testing strategy for testing your javascript in each browser.

If all of this seems super overwhelming, then just stick jQuery. :D