Twitter: Twitter is the birthplace of modern hashtag usage — as such, its hashtags are more versatile than other sites' (see “Tone & Voice,” below). Twitter hashtags are mainly used to denote specific topics of conversation; the “Trends” sidebar of your Twitter feed curates a list of hashtags you might be interested in, based on your tweets.
When you search for a hashtag on Twitter, there are three ways to filter the results. The "Top" option displays the most relevant and popular posts, including those from users you don't follow. "All" shows you every tweet that uses the specific hashtag in real time, and "People you follow" will only display results from users you are following.
Facebook: Facebook only recently added hashtag support in June 2013, and the practice has not picked up much steam. Nevertheless, clicking on Facebook hashtags will take you to a list of posts containing the same hashtag. The results are not limited to people you know.
Instagram: Hashtags can be used to complement photos shared on Instagram and help you discover new accounts and pick up followers. Some hashtags were created specifically for Instagram photo challenges — #ThrowbackThursday, for example, encourages users to post retro photos. Vine uses hashtags in the same way — try accompanying each of your Vine videos with at least one hashtag to maximize shareability.
Google+: When you click on a hashtag in Google+, the search results will include the original hashtag as well as posts with similar tags and keywords. Google search results display on the left side of the page, while hashtag results from within Google+ appear on the right. Google also gives you the option to search within Facebook or Twitter.
Tumblr: Tumblr posts have a special “Tag” section where you can enter tags. These tags function like Twitter hashtags, organizing posts by topic, but the hash symbol is inserted automatically. Hashtags included in the main body of a post are not transformed into links.
Pinterest: Use Pinterest hashtags to mark and search for content. Click on the hashtag in a pin description to navigate results that contain the exact hashtag, plus pins with the same word or phrase in the description.
Curious which hashtags are trending across social media? We prefer to use Hashtags.org which gives us information on which hashtags are hot in real time (and which ones of course, you better have to avoid).