Yes you can, not through an official setting unfortunately. But as TylerH said you just say "I don't like this tweet" on a few of the tweets that you see because "person X liked this", then refrsh your feed and they're all gone.
Maybe after 6 months-ish they come back, but you notice it really fast since suddenly your twitter feed sucks. Just do the "I don't like this tweet" trick again.
The only 'likes' I see now is if multiple people I follow liked a tweet from someone I also follow. Usually those are good quality.
Alternately, you can control whether you see what individual people you follow are retweeting with "Turn off retweets": https://twitter.com/following
>/following yea really wish you could do that with likes too!