I wish I had grown up in the iOS age. I still have lots of old media (movies, music, etc.) that was ripped from CDs, recorded on actual video cameras/still cameras, and backups of all that stuff as well. So here's my setup:
MP3s: All on a folder on a hard drive on my tower in the basement. Those are backed up to a 3 TB external drive as well and also every single one of those songs is uploaded to iTunes Match. So I can play them on the Apple TV, iOS devices, on our iHome dock, etc. We also have an iPod Classic with 120 GB and it holds absolutely everything--makes a very good go-to device when we're on the road and, for example, don't have a good 3G signal to download iTunes Match content.
Movies: Same deal. I turned all of our old home movies into digital files. We can watch them through Home Sharing on the Apple TV or we can stream them to the PS3/Xbox if we want as well. For watching regular movies, we are all Netflix and iTunes. We are not big fans of amassing a huge collection of movies, so we just watch iTunes or rent them on iTunes on the Apple TV or on Vudu on the PS3.
TV shows: We are cord cutters, so we're big users of HuluPlus. I am thrilled that they now support AirPlay, so we can AirPlay it to Apple TV or use the app on PS3/Xbox.
We are more or less almost exclusively streaming everything now. We don't have a cable subscription--just internet. And, much to our delight, still get more content than we could ever watch/hear.