myetherwallet - all types of erc20 coins/tokens.
See the full list here:
https://etherscan.io/tokensFor other coins, using their own recommended wallet/exchange usually works.
Same idea here, check the coin if it's under ERC20, just don't ever ever share your private key cause you have only one...
If your joining campaign it will state also if their coin is covered by ERC20 and advice you to create a wallet compatible to their campaign coin so its not an issue, they will provide you a link (usually from the campaign manager and not anyone else)