Transit is a fantastic free plugin that will provide you with the smoothest transitions using jQuery. The plugin is easy to use and will animate any element in both 2D and 3D transformations.
Multi-screen.js will provide you with animated transitions to switch between "pages." Basically, it's a unique way to create a single-page site that has the illusion of having multiple pages because the user is able to flip through the content smoothly and easily with the help of Multi-screen.js.
Fluidbox is an image-enlarging plugin that allows your user to click on an image to enlarge it, and when the image enlarges, it does so using a nice transition effect. Perfect if your project has a lot of plugins that you want your users to be able to enlarge without it feeling clunky. The plugin also supports responsive designs.
Blindify is another transition plugin that can be applied to images. The aim of the plugin is to allow you to create image slideshows where the transitions are a vertical or horizontal "blind-effect" -- so it sort of resembles animated window blinds.
5. Square Menu
An interesting take on the menu concept, this plugin helps you build a square (or rectangular) menu that opens at a single click, and when it opens it does so using a beautiful, customizable transition.
A cool way to use transition effects it to apply them to pop ups or dialog boxes, which is exactly what the Dialog plugin does. With Dialog, you can apply smooth transition effects to any pop-up, so that the pop-up effect is sleeker and less jarring for the user. This plugin is ultra lightweight.
Wiper is another plugin to use when creating image slideshows. This slideshow plugin not only offers cool, wiping transition effects for your slideshow, but it also provides a very unique slider navigation (see in the screenshot above all the bars in the top left corner that say "sample" -- clicking one of these will reveal a previously viewed slide).