The only other place I’ve ever used a “like” button is on YouTube. I use YouTube almost exclusively for its “how-to” videos, and occasionally I’ll watch one that I might want to watch again sometime. If I “like” it, I can easily find it again because it is listed in my profile with all the other videos I’ve liked in the past.
Of course I could use their search function, which is much the same as the search function here. The main drawback is the number of hits you receive, which can be quite a chore to sort through, just like the search function here. Also, it is sometimes difficult to define your search so that you get the results you were looking for, especially when you have only a vague idea of what you are looking for in the first place. But if you know you're looking for something that you “liked” in the past, it is easy to find.
For me, this is a much more useful feature than just expressing appreciation for some video or post that you thought was well done, although from YouTube’s standpoint, they no-doubt use “likes” to filter the results that are shown when you open the app, and advertisers use it to determine whose channel they will spend their $$ on, neither of which has much if any application here.