What are ways to show phone conversations?
I like to think of alternate ways to do things, so here are a few.


One variation of the split screen is a picture-in-picture layout, where Caller B is in a small (often rectangular) box overlaid on the main shot of Caller A.  
Another variation of the split screen is a "cloudy" picture-in-picture, where Caller B appears as a cloud-shaped image with fuzzy edges overlaid on the main shot of Caller A, usually floating above Caller A's head. This is sometimes used to make it look as though Person A is thinking of Person B, but I'm pretty sure I've seen it as a phone call too.
If the call occurs in present day, a video call on a computer screen can show Caller A and Caller B in a variety of layouts.  It could even include Callers C, D, E, etc.
Some scenes only show Caller A, and Caller B is heard without being seen.
In the movie The Player, there is a creepy scene in which Tim Robbins calls a woman he's attracted to / stalking.  He's on his cell phone, outside of her house, at night. She can't see him but he is looking in through her windows while they talk. So there are some 2-shots that show both of them on the phone simultaneously. (It's briefly included in the trailer at 1:10.)