I get so many emails (mostly as part of email lists) that the way I process them is to simply scan my eyes down the list of messages, looking at sender, subject, and the first few words. I only actually open a small fraction of them.
In my experience this method is unfortunately error-prone. My eyes somehow blow by messages and I only discover them when someone either asks in person why I haven't responded or, worse, some bad consequence develops (i.e. a service is interrupted because the registered credit card expired and I never responded to the warning emails).
This is not a question about how to process email in general, which is a larger issue and has been addressed before, but more narrowly, how to make 100% sure I see the very few super-urgent emails ASAP.