We have three active cards -
-MBNA/BOA (after they merged) Mastercard that I have had since college
-Discover that we have had for at least 6-7 years (this is our cashback card)
-AmEx we opened last year to get a 0% rate for DH's tuition - we'll close it after we pay the balance off
I've had probably 5 or so more over the years. I opened a Sears account twice to get discounts on major purchases. I also opened an Amazon one once to get $25 off my purchase. DH had several that he signed up for to get free merchandise in his younger days, but those days are gone
We do not plan to get any more, but to keep our two main cards indefinitely.