These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: The Fault in Our Stars
Ho Yay: Isaac points out Augustus's "physical attractiveness" multiple times. Also, Augustus claims that his hot body caused Isaac's blindness.
And on the dubiously canonical Q&A blog that John Green runs (see main page for link), Isaac is referred to as both "gay" and "a [future] ballerina." Both are said in jest, but still.
Memetic Mutation: This book (not to mention the author) is massive on Tumblr, mainly for being a massive Tear Jerker and a major source of feels. A common Running Gag is for newtime readers to document their first readthrough of the book and the progressive regression into a blubbering puddle of tears.
"My x are x that I cannot fathom into x."
"I <verb> the way you <verb>: slowly, then all at once."
The Woobie: Both of the leads, plus Isaac and Hazel's and eventually Augustus's parents.
Jerkass Woobie: Van Houten. Yes, he's a drunk asshat, but you have to admit he is sort of a tragic character.