I frequently see recommendations to regularly run sp_cycle_errorlog, so that the errorlog doesn't become huge. My main concern with that is that the errorlog contains valuable information. When I do a health check on a SQL Server machine, I want a few months worth of errorlog information available. I typically use my own scripts for this, ...

How often do you do this? Look over each message (type) in the errorlog file and determine whether this is something you want to act on. Sure, some (but not all) of you have some monitoring solution in place, but are you 100% confident that it really will notify for all messages that you might find interesting? That there isn't even one little ...