When Google Realtime was launched, it would show a lot of results from Twitter. It showed Twitter's awesome dominance on almost all events which were important to be followed in realtime. Then things between Google and Twitter went sour and Google had no longer access to all data from Twitter.
I use Chrome and HashPlug extension works seamlessly to give some related tweets in an unobtrusive manner with my Google search results.
Below is a screenshot of me searching for "Diwali Festival" on Google. Notice the realtime tweets streaming in the right hand side.
If you are signed into your Twitter account on your browser, then you can even retweet, favourite or reply to a particular Tweet from the feed directly.
If Google is showing a related page with its knowledge graph for a particular search term on the right hand side, it gets automatically readjusted below the twitter stream.
Usually this sort of Twitter stream would be very useful while using Google for information about an unfolding event like a sporting event or a breaking news story.
Thanks to @Fenoplix for the tip. Do try out HashPlug and drop in your comments.