I have friends who have a tendency to ABUSE the share button. I don't want to see the stuff they share, but I want to see everything else.
How can I do this, or is this something I can't change?
I'm not sure if you can block only shares and likes.
What you can do, though, is clicking the downward arrow on a post by one of those users, and selecting "Only important" from the "Subscribed to X" section.
True, you will see very few of the things they post (guess what? Only the important ones!), but odds are good that if they constantly share dumb crap, they won't post anything worthwhile of their own either.
You can change what types of stories get posted to your newsfeed.
When a friend posts something, you can:
The resulting menu will not only allow you to select "Only Important" stories like @sm's answer states, but it will also allow you to choose what types of stories appear from your friend.
In your case you might try unselecting "Comments and Likes" and "Other activity," but I suggest fiddling with the different types of stories and seeing which selections best serve your preferences.