Shatner and Nimoy are without a doubt best friends, if not as good as family. It's been documented that Nimoy was really supportive during Shatner's marriage to Nerine Kidd who suffered with alcohol problems. Nimoy would go along with Nerine to AA meetings and it's been mentioned that Nimoy supported Shatner following the death of Nerine.
Things like that are one of the many reasons I have a lot of respect for Leonard Nimoy. Despite being a household name and creating an influential character, he never lost site of being a respectful person. He went out of his way to help his best friend's wife out and provided the couple with an enormous amount of support. Nimoy is universally liked by TOS cast and even used his clout with the producers to ensure that they all got a decent amount of screen time and salary.