I probably open up 3 - 6 cards a year and cancel about that many too each year.
These are in my wallet
Chase Freedom for the 5% category bonuses earning Ultimate Reward points
Chase Sapphire preferred for the 2% on dining and travel and to dump my Freedom UR points in that account so I can transfer them to airline miles
Chase Ink Plus business for the 5% on electric, cable, phone and office supply stores. I buy store or Disney gifts cards at office supply stores and get 5 miles per $ on my shopping and
Disney vacations.
Starwood Preferred Guest - points transfer to over 30 airlines, Amex offers
Citi Prestige which I just picked up for the bonus recently
These are in the "sock drawer"
Amex Everyday no fee to keep my Membership rewards active from a previous Amex that I picked up for the bonus (100,000 mile Platinum) and then cancelled. Didn't want to lose the points but didn't want to pay a $450 fee
2 no fee Discover cards in a drawer that I only use if they give me a great incentive like spend $1000 and get $100 cash back
Disney Visa no fee - used to book Party for the Senses in advance of regular booking
Capital One Venture which DH and I picked up to get $800 in excursions on the Disney Norway, Iceland Scotland cruise last year. Haven't decided if I will keep it or cancel it yet.
Barclay Arrival no fee card which I just downgraded from the Plus so I can keep a card with chip and pin for travel in Europe
Citi American Airlines Advantage gets me 10% back on redeemed miles and free checked bags
United Mileage Explorer card - card holders have access to award flights that are not available to those who don't have the card
Club Carlson card - 40,000 points every year on your cardholder anniversary date = free hotel stays overseas
Marriott Rewards card - free night each year in a category 1-5 room which is worth more than the fee
Hilton Amex - gold status and part of my 5 year plan to stay in overwater bungalows in Bora Bora for a week which is going to need about 7 credit card bonuses to accomplish LOL
Amazon card no fee - sits in the drawer, buy gum or something with it once a year.
Costco card which is now a Amex no fee green card which I will probably cancel so I can get a rewards earning Amex in its place