For store memberships: I ask the cashier "Do I need the card, or can I just type in my cell number?" (I only give the cell number out because nobody calls cells, and I don't want to be bothered at home by a store). All the grocery stores and the 1 store at the mall I have a reward card for can take my phone number instead of the card, so I threw the cards in the trash. I still get the rewards.
For the Blockbuster and the library, they take my drivers license as well as the cards, so I threw away the cards---I always have my license on hand, so that's easy.
For places you don't go everyday: the zoo, arboretum, museums, season passes to an amusement park, stuff like that....AND the gift cards---I put them in a little file thing. At Walmart (or anywhere---last week Target had them in the $1 section) in the office supplies thing, they have little accordian file things that are just a bit bigger than a checkbook, and it has 9 tabs. I have one and labeled it to keep my coupons (food, bath, cleaning, kids, misc, going out are my coupon labels). There were several other tabs, so one of them is for gift cards, one for "passes", another for little recipes I pick up while visiting a friend, or passed out at a store, and want to try. (They have to EARN a spot in my recipe box, lol...and I try at least 1 new recipe every week, so that works fine). I keep my little file on the desk unless I'm going out shopping (I make a list ahead of time, pick out the coupons I'll be using on the shopping list, and slip the ones I'm using into the very front pocket so I'm not sorting through a bunch of junk in line). But also, yeah---if we're going to make a little trip to the zoo or wherever, just pick up your file and pull the pass out of the "passes" tab.