A decent user interface
An interface that fits the feel or theme of a VN is always a nice-to-have.
A backlog with jump options
It is a cardinal sin for any VN not to have this feature.
The ability to change the font
OsakaMono trumps all.
Infinite save slots
I have a tendency to save quite often, always in different slots. Many VN's are not quite accommodating to this particular need.
Scene recollections
Being able to replay certain scenes (besides h-scenes) in a VN would be very nice, and would actually lower my need for infinite save slots.
Skip to next/previous choice
This comes in handy when I finish the first route in a VN and would like to start up the next one as soon as possible.
Decent sound/music mixing
Essentially, lower the music volume when a character speaks so that I can hear them properly.
Dynamic character sprites
Like Ren said, it helps add depth.
A fully-realized protagonist (visually and vocally)
A protagonist with their own character sprite and voiced lines just helps with the immersion.