With Joomla beginners there often is a tendency to install a lot of extensions, especially front-end extensions like galleries, social media feeds, video plugins, etc., because they look so nice. Especially extensions connecting to external sources, like Facebook, Twitter, Picasa, Flickr, etc can seriously extend the load-time of a page, because the external connection takes additional time.
However, really every additional extension will always take up some time. Well programmed extensions will take a minimal amount of time to load, so it also pays to check good sources for your extensions. Of course, in most sites you will have to use some extensions, you can hardly build a ticket-selling website without an event manager, but whether you need a Twitter feed on all your pages is worth considering. Maybe you just need it on your contact page, which will free up the homepage.
Avoid sliders and carrousels
Sliders and carousels should be avoided as much as possible. Though web designers and the customer who ordered the website often find these very attractive, actual users that visit the website often ignore them, or even treat them as ads to be blocked (banner blindness). Usability tests have proven that they are mostly very ineffective and that no more than 1% of users evers clicks on a link or feature in the slider. You might want to check www.shouldiuseacarousel.com.
Remove MooTools / Jquery
In those cases, you could try to prevent MooTools from loading. Either do some smart programming with a template override, or use an extension like the Mootools Enabler/Disabler Plugin. It even allows you to still load the library under certain circumstances.
In Joomla 3, Jquery is loaded. Especially for responsive sites, it may be necessary for the Bootstrap responsive menu. Keep in mind though whether you really need it.
I recently published a blogpost with a comparison test between different template providers that you may find interesting.
Social media share buttons
In a previous version of my site, I only linked to an external URL, including the necessary data in this URL, as you can see in this example for the Google+ share:
Using this, all your content can be shared, and it requires no external connections and bandwidth / latency at all. You can use this technique for most platforms, including Facebook, Twitter, Google+. Recently, I switched to a nice plugin called Fast Social Share, from the same developers as J-sitemap. This loads your buttons with standard behaviour, but it does so in a way that it only loads the buttons when the page is fully loaded: