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I have 10 and I wish I had less, maybe 7.
I created a vertical calendar in Excel with rows 1-31. Next to each row, I write "Citi Forward due", "AMEX due", etc...
Of the 10 cards, 2 are sockdrawered. But I always get a nagging feeling that I left an automatic annual renewal on them, so I always check online to make sure the balance is zero.
Once you are out of the madly apping phase, that usually means you don't need to micromanaging your FICO score with utilization concerns.
So then what you do is set all of your cards (whether 2, 10 or 200) to autopay in full on due date. (This of course assumes your spending is under control, if not, the number of ccs isn't the problem you should be focusing on!) Then with no effort, everything is taken care of, no late fees, no interest charges.
I think everyone should do this for safety as default anyway, and then, if you are apping/applying for loan or mortgage/just want to present best score, you can make early payments to make the balance 0. But unless you are apping, no need to do this much!