22 active right now.
3 or 4 that we use for rewards, although all of them give something. Since many of them have non-public promotions, I re-assess every quarter. For 3/4 of last year, I'd only use the "right" card for 10% back. Now, I have 3 cards giving me 5% back.
I have a spread sheet to keep track of closing dates and last purchase date for tradeline sales and low balance forgiveness.
There are some useless cards in the mix that give me no extras back, so they just sit gaining age.
I'm one of those who tapes on the card notes of percentage back and on what. For example, a couple months ago, it was 10% back on restaurants, gas and groceries. Since grocery stores sell gift cards, I could buy gift cards to other places (usually with a bonus for gift card purchase towards gas) and then extend the category to other things. I bet you didn't know a chainsaw is a grocery. It is when I'm buying it. :D