There were probably combat applications for the Vanquished Tentacle back in the day. Like, it summoned a tentacle that would fight for you and stuff. But nowadays, I mostly see it used by blood elves in Silvermoon for roleplay. (Look, I'm not judging, I'm just saying.) The tentacle that is summoned is large and green and longer than your average tentacle. The truth is that if you're looking to play a warlock in touch with insane elder gods, you could do worse than to use the Vanquished Tentacle as a roleplay prop.
Or you could drape yourself in the blood of Yogg-Saron, but who would be dumb enough to do that?
Name Vanquished Tentacle of C'Thun
Attributes Summons a Vanquished Tentacle to your aid for 30 sec. (3 Min Cooldown)
How to get it Kill an Elder God. It used to take about 40 people, but you can do it with a handful nowadays. I've not yet heard of anyone soloing it, though.
How to get rid of it It sells to 10 gold. I'd have thought one's sanity worth more than that.