Is there any way to create a link or "saved profile" for launching an EC2 instance with a given configuration?
I'm aware of the mechanism where you can create a link to launch a given AMI, i.e. http://console.aws.amazon.com/ec2/home?region=us-east-1#launchAmi=ami-XXXXXX. However, there are still a lot of configuration steps left (instance type, security group, etc).
Is there anyway to automate this process, in such a way that it can be launched by an arbitrary Amazon account?
You should look into AWS CloudFormation.
The idea is that you create a JSON "template" document that describes the resources (EC2 instance, EBS volumnes, security groups, RDS services, etc) for a given "stack". The JSON document can be more-or-less independent of a specific account. You can also specify configuration prompts (which region to launch in, etc) to collect additional information from whomever is actually launching the stack.
From the AWS CloudFormation page: