Like Bitcoin, Ethereum has fees for every transaction.
Unlike Bitcoin, Ethereum smart contracts require additional fees for every call to the smart contract. The BitGo multi-signature smart contract in Ethereum incurs smart contract fees in three cases: (Gas Used * Gas Price * USD/ETH)
Wallet creation: 1106780 * gas price * price of eth
Receive address creation: 240160 * gas price * price of eth
Sending transactions: Depends on the address you are sending to.
Please note that these fees are calculated based on the default Gas Price used by BitGo which aims to get confirmations within 2 minutes. API users have the ability to adjust the Gas Price and bring down costs. For example, receive address creation costs can be brought down by lowering Gas Price to 4 Gwei, as long as you are not concerned about how long it takes for your transactions to confirm.
The Solidity code for the BitGo smart contract can be found here.