I have a Nexus 4, and I would like to be able to switch it to vibrate mode without having to look at the screen or unlock it. My previous phones had this ability (my iPhone had a switch dedicated to this on the side, and on my flip phone before that I just held down the volume down button). I've found this feature pretty useful in many situations where I realize after the fact that I want my phone to be silent, but I don't want to show that I'm silencing my phone (movie theaters, churches, meetings, etc.). I keep my phone in my pants pocket, and the other two phones allowed me to silence them without even removing them from my pocket.
I've tried holding down the volume up, volume down, or power buttons, but that doesn't do anything. I know that there are apps that I can configure to automatically silence based on my location, time of day, and/or calendar items, and while those are useful they still don't give me a universal way to silence the phone with minimal interaction. A home screen or lock screen widget won't work for me because my work requires that my phone lock itself, and doesn't allow me to put widgets on the lock screen.
I'm also not interested in rooting my phone, but a free or paid app (preferably on the Google Play store) is fine. Really, an ideal solution would be an app or setting that allows me to press and hold the volume down button (while the phone is still locked) to put it in vibrate mode.