Ahem…
Although Aperture Science may have this thing locked up with that ungodly ratio Choie provided us.
Sorry to bump this thread, but we have a new winner:
Rick Perry’s ad with 3.4 million views.
16270 likes
557411 dislikes.
Ratio: 0.0291
Hm, not that surprising with hindsight that Rick Perry would manage to get such a terrible ratio.
Sorry for the late reply, this must have gotten bumped when I was away from the internet for a few days or something, I don’t know how I otherwise would have missed it.
Take a load of this then 
2278 likes/5 dislikes (455.6 ratio)
Béla Fleck and the Flecktones - Schratch and Sniff
281:1 - 68000 views
Béla Fleck and the Flecktones - Big Country
125.5:1 - 430000 views
A Moment so Close - Bela Fleck and the Flecktones
infinite - 11000 views
Bela Fleck and Flecktones - Ah Sho Dekio (with Kongar-ol Ondar)
infinite - 1500 views
Does it show I really like this band?
900:1 Gaseenhauer, I’m sure the 20 people miss-clicked
Geez, and I thought I was going to do well with a 111.5:1 ratio for The Secret City of London (Part 1)
I should pay attention to whether strangers liked or disliked something I’m looking at? Because…?
Because evolution (if you believe in it) has hardwired us to care about the opinions of our fellow members of society.
Also, I think it’s really nice to find something that even angry tween trolls can’t help but give the thumbs up to. 
‘Freedom’ from the Django Unchained soundtrack has the greatest ratio for any kind of music I’ve heard on YouTube (with minimum view of 1mill):
(~300:1)
I’m not going to go comb over them all to find the most striking examples, but when I was watching lonelygirl15 a year or two ago, the amount of dislikes on all the videos that were posted after it was revealed that it was a produced web series and not real were absurdly high.