I carry 5 cards.
US Bank Cash+ Visa Sig
You could make the arguement that I carry 6 as I keep BoA Cash Rewards in the car. It is used exclusively for gas.
BofA Cash Rewards Sign Visa
Wells Fargo Visa Mortgage Rebate Card
still trying to get an Amex
I usually carry the Amex BCP & PRG
Usually, I carrying the following. A business card, SPG (only domestic), CSP, and HSBC Premier (if abroad). This is assuming I've meat the $10K spending my Ritz card for Gold Elite, otherwise I'll carry the Ritz for the initial $10K.
I carry 2 for work, 2 for my biz and 5 personal
3 for now: Cap One Platinum, Cap One Cash Rewards, Walmart Store Card ... if they approve me for the Speedway Station Card it'll be 4.
I currently carry all of the ones listed in my signature, but I may be closing my BofA card soon. I simply don't use it, and dealing with BofA is painful when compared to Chase or JPM.
I would recommend leaving open something other than a Chase card. If something happened between you and Chase, you would be without a card. I think it would be a good idea to have a couple other cards from different issuers just in case.