My ISP provides an option to pay for a fixed IP address. What are the advantages of a fixed IP address? This relates to a home connection which will be used for general browsing, movie download / streaming, and video calls.
If they make you pay for a fixed IP, usually that implies they allow you to hosting content from your network.
I host a media streaming application called Subsonic, Which lets me stream music from my home computer to wherever I am. I also use it to ssh into my system.
Note: Depending on you connection type, your IP rarely changes anyway. On Comcast, Ive had the same IP for about 2 years now, so for me theres no real need to pay for a static IP