Aside from Judgement at Nuremberg, you should check out Shatner’s work in The Brothers Karamazov.
Shatner was actually a highly regarded actor before Star Trek. He won acting awards, and got a shot on TV because he had been in three successful Broadway plays where his acting got good reviews. His early work on TV was in ‘artistic’ productions like Circle Theater and The Twilight Zone.
The thing is, like a lot of other actors who had a career-defining role, Shatner became a bit of a caricature of himself as the years went on. Leslie Nielson is a good comparison - the young Leslie Nielson was an excellent character actor, completely unrecognizable from the over-the-top ham he became later, when his role in Airplane! typecast him.
I’ll bet you that if Shatner was given some serious dramatic performance with a high billing, he could pull off a very good performance. Say, if Quentin Tarantino had a juicy role for him as a washed-up cop who does despicable things or something. I’ll bet he could turn the ham off, and do something serious if he really wanted to. But at this point in his life, he may not want to. He’s getting up there in years, and I get the feeling that he really likes being William Shatner.