Most coins will need an Eth (Ethereum) address or what's known as MEW/Erc20.
You can get a free wallet from:
MyEtherWallet.com: Your Key to Ethereum
and follow the instructions carefully (it's very easy).
Then when you sign up for the free coins you give the same wallet address for each airdrop - keeps it very simple. But here is a video to show you how to do it, step by step:
You can continue to use that to view your coins or you can install metamask as a Chrome extension (makes it easier to view/send/purchase).