Each VPC can have only one Internet Gateway.
Each Internet Gateway can be attached to only one VPC.
If there is no Internet Gateway attached to a VPC, then the VPC will not have any connectivity with the Internet. This can be useful for 'internal' applications, such as Dev and Test. The VPC can be connected to a corporate network via Direct Connect or VPN, with no risk of being exposed on the Internet.
While the VPC Wizard automatically creates an Internet Gateway (for most scenarios) and attaches it to the VPC, you can also create a VPC manually without an Internet Gateway.
There is no charge for an Internet Gateway. It is a logical connection rather than a physical device.