Back when I ran Chicago on the Cheap, I was on the hunt for things to do with incomplete decks of cards. Sure, you can use them for things like bookmarks, but who needs 49 bookmarks? They are too slippery to build a house of cards. So what?
I have finally come across two games that can be played with incomplete decks of cards and that can also be used with several mis-matched decks of cards together: Crazy Eights and Bullshit. (You can use other names for the latter to protect the sensibilities of those playing.) Both allow you to play without matching cards exactly or grouping them in precise amounts. Next time you have people over, combine your mis-matched and incomplete decks, declare jokers wild, and go to town.