I am connecting 15 I/O expanders to my Arduino. The I/O expanders all share the same 5V supply. Do I need capacitors on the V+ pins for every IC?

It is highly recommended. And the caps should be as physically close to the expander chip as possible (very short leads).

0.1uF 50V ceramic caps are used all over. I buy them by the hundreds.

This is what I suspected but wanted some reassurance. Thank you.