The girls have been building a fishing shanty, so we implemented this method for joining cardboard. I demo-ed it at a cardboard play day last fall. Here's the lowdown:

PROS: rEAlly cute, fairly strong, reusable, made from reclaimed materials, virtually free

CONS: takes a fair amount of dexterity to thread buttons and twist, and sometimes hard to thread through the cardboard without a helper. Only suitable for non weight-bearing construction.

What you need: twist ties (the longer and thinner the better) buttons, a screw driver

What your kids will call you: AWESOME.