DAMN best hugs? This is so hard, there are a lot of good ones. HM's are def blake sibling hugs, linctivia and bellamy/raven but well, I had to pick five.
No time to pretty this up so I'll just post this quick. (sorry, stealing gifs from other people hope thats okay!)
BEST HUGS
#01. Bellamy&Clarke | 4x13
I mean, the hand in the hair and the tears and just
sdfdsfdsfds. It's so emotional and it's adorable that
he was there to comfort her. 
My precious otp. <3
I didn't even realize this was my favorite until
I rewatched it. lol.
#02. Bellamy&Clarke | 2x05
Everything about this moment was like a movie scene
I swear. How she sees him, then runs into his arms.
They were so happy to see one another and after that
long time apart it was so great to see them back together.
#03. Bellamy&Clarke | 3x13
Wow, okay, so I am super biased during this freaking
topic but I just cannot help myself, Bellarke own me okay?
This hug was just super sweet as well, and I love that
Bellamy finally forgave Clarke. She's his soft spot.
#04. Bellamy&Octavia | 2x04
Not sure what to say about it really, it was just a very
sweet hug between them and I was really really
happy to finally see them reunited.
#05. Murphy&Raven | Season 4
Forgive me for not remembering the episode number
as I've only seen the season once. But of course
I had to include this because these two are my
new ship on this show. I really hope it goes there
eventually because I just adore their dynamic.