Fun
Linguistic research isn't all collecting and analysing data, writing papers, and teaching. Don't get me wrong - all those things are awesome. But there's sometimes stuff that is more transparently fun (and yet still related to all that academic things). Some of these are my own creation, but most are things I have found. Check it out ...
My own
My Twitter account, @TimPhon. Also lists of other linguists, like my list here or this much more extensive list by Jen Nycz.
The Larynx Quest, a brief adventure in Minecraft.
Others'
A Phonation Mode quiz. Find out which phonation mode best matches your personality!
Speculative Grammarian. For those who want a deep, deep dive into linguistic in-jokes.
Podcasts
Lexicon Valley: a well-crafted and entertaining look at serious questions of language
Grammar Girl (podcast and blog): a wonderful example of prescriptivism done well
Lingthusiasm: a podcast about various topics, hosted by two enthusiastic linguists
The History of English: a long-running podcast about the history of the English language (starting with Proto-Indo-European)
The Vocal Fries: A podcast exploring linguistic discrimination
En Clair: A podcast about forensics and linguistics
(Please let me know about others that you have come across.)