I process them daily. Usually in the morning with my morning coffee but sometimes in the evening (actually I play with the time of checking now to find what suits me better). It takes about 1 hour to process all the inboxes (notes in my phone, three email inboxes, electronic inbox on the laptop and physical inbox in my briefcase).
I don't process it enough - only about 2 to 3 times a week - and that stresses me, because I actually think about if there is anything urgent (nevermind important) in my inbox. I'm sure if I did it within the time frame suggested, everything would be clearer.
I tend to empty my paper inbox once per day (first thing in the morning). Typically, I'm the only one adding things to my inbox, being self-employed, so I don't worry so much about things sneaking in there when I'm not looking. My e-mail box gets processed about 2-3 times a day, and my voicemail usually gets processed as soon as I notice that I have a message waiting indicator.
I think the key here, at least for me, is to process exactly as often as it takes to keep the quantity of unprocessed stuff at a manageable level. I have a friend who's a paralegal in the military, and I doubt processing her inbox only once per day would be adequate. On the other hand, I know people whose work entails large stretches of focused work with little external input, and so once every other day might be more than they need. One thing I've learned to do is to pay attention to my internal "worry meter": When I start to feel anxious about what's accumulating in my inbox, it's time to process it.
I have one physical inbox at work which I leave empty at the end of every day. Wasn't always that way but it now bugs me to to leave stuff hanging around (what DA describes in audio somewhere as the yuk factor). Physical inbox at home is troublesome - I scan it every 24-48 hours, process some stuff but use it too much as temporary storage. Need to get better at that. Email inboxes are checked three times a day and always at zero by day's end.