I can no longer in good faith recommend this add-on(Search Predict for Trakt.tv) as I found that it randomly causes Trakt.tv to crash... at least on Firefox.

Update: comment only left for reference.

I found that it is available in Firefox too...
https://addons.mozilla.org/en-US/firefox/addon/search-predict-for-trakt-tv/

Lo and behold, a wild add-on appears in the Google Chrome Web Store to accomplish this very thing! It lacks the elegance of the native code but it gets the job done all the same.

https://chrome.google.com/webstore/detail/search-predict-for-traktt/aelihdggbimbhmgnjghphaliainkknid

Perhaps you can consider https://www.algolia.com/ doing the heavy lifting. And negotiating a sweet deal by keeping their brand on the search box (same as Producthunt did).

"Visually might be easy to add, but performance wise it takes a bit more time to do this. Something we plan to add in the future." @ February 22, 2015 12:32 AM

Trakt is great in so many ways, except one: the search. I understand it takes more time to implement this omnipresent predictive search feature, but come on guys, more than 3 (three!!) years have passed and we are stil waiting...

It would be nice to have autocomplete in the search-bar making it possible to jump directly to the show/movie you are looking for. An example of what I mean is when you enter an article name into the search bar on a wikipedia-page a list of results appear below making it possible to skip being referred to a separate search results page.

I like Trackt, but I've always been disappointed with its search bar. Not only does it not do predictive search, but it's also not resilient to typos and misspellings. A service like https://www.algolia.com/ or a customized instance of Solr could probably alleviate these kinds of issues.

that would be sweet

Visually might be easy to add, but performance wise it takes a bit more time to do this. Something we plan to add in the future.