Mysql – Amazon RDS suddenly not working and unable to connect

It's unclear what you mean by "wildcard" - there are two types of entries in the security group that you can make - a CIDR block and an EC2 security group:

With a CIDR block, you are specifying an IP address or IP block. The most popular CIDR blocks are /32 which is an individual address and /24 which is a block of 256 addresses (a "class c") - see http://en.wikipedia.org/wiki/Classless_Inter-Domain_Routing for more details on how enter your IP blocks. To open to all IP addresses (i.e. "a wildcard IP address"), you could use the CIDR block 0.0.0.0/0 but Amazon strongly discourages allowing global access to your RDS instance http://docs.amazonwebservices.com/AmazonRDS/latest/UserGuide/Overview.RDSSecurityGroups.html however it might be something you do temporarily to help debug the issue.

With an EC2 security group, it is effectively a wildcard - all EC2 instances that use that EC2 security group will have access to your RDS instance.

Documentation on updating RDS groups is here: http://docs.amazonwebservices.com/AmazonRDS/latest/UserGuide/USER_WorkingWithSecurityGroups.html

It it worth noting that it might take some time to actually be "authorized" after you create the RDS security group entry. You might want to check the "Recent Events" tab in the AWS console to see the progress of your security group settings.

By default RDS does not allow any connection that is not specified within the Security Group (SG). You can allow based on CIDR addressing or by Amazon account number which would allow any EC2 under that account to access it.