The ability to record any game footage you want on these consoles is something that means a lot to me. I know some people find these extra features a waste, but man, I have enjoyed using it on both consoles. Right now, its one of my favorite features of the next gen consoles.
I like saving epic moments, especially when playing with my friends, but I also love being able to easily record weird events or obvious bugs/glitches that I run into.
Throughout my years of gaming, I've thought to myself "man, I wish I had that recorded" after a great moment or a hilarious glitch. It has always been too difficult or too expensive to do. In recent years, I remember when EA first added the ability to record clips and upload them from within their college football games and I really enjoyed it. My friends and I play a ton of those games and having the option to save short clips of particular plays during a game was great. Yeah the quality was fairly crappy and you were limited to just the list of plays during a game, but it was something.
Now we are really close to the perfect system imo. All that is left is for MS and Sony to drop the arbitrary limits on recording time and allow quality control options for me to be set. Still, its great to have. Now when something completely bizarre happens in say AC4, I can save that. When I have an epic finish in a game of KI, I can save that. When I make a great run through Resogun, I can save that.