It bugs me when people ask questions like “what framework to do use?” or “what are some plugins that you use on every project?”.
Frameworks like bootstrap, foundation, and others are all well and good, but there’s bound to be a whole tonne of stuff in there that you’re not using. Perhaps they are suitable for prototyping, but my feeling is that there’s going to be far too much bloat for a production site. Not to mention UI patterns looking and behaving like default. Consistency can be a good thing across the web, icons are a good example, but it would be boring if everyone used the same sliders/accordions/navigation etc.
I also think they can harm creativity. When it’s so easy to throw an accordion at a problem it’s possible to miss other, potentially more appropriate and effective, solutions. Solutions that are bespoke to your site, that may add personality and character – otherwise lacking from an out-of-the-box module.
As for jQuery plugins, I don’t default to any. Unless I have a specific situation where it would save time, and not cost too much in terms of code bloat. FitVids is a good example. There’s no way I’d rewrite the code to make video’s elastic, and FitVids is pretty lightweight without the need for many options.
jQuery slider plugins can be among the worst offenders, many of them have way more options than you’re ever going to use. Much better to either code it yourself or take (and cite) only the bits of code you need.
Use what you need, and nothing more.