I am a complete newb to AWS. I have a MYSQL database that is about 4TB and growing each day and would like to move it to AWS. According to this link the maximum allocated storage size is 3072 GB. How can I run my DB on AWS? (I can think of a dozen of AWS's customers that have a DB > 3TB so there must be a way, right?)
3TB is massive for the majority of Amazon's customers
The majority of Amazon's customers consume far less than 3TB databases in fact the majority will use less than 5GB. The problem with with databases or generally those offered by services such as MySQL is that the bigger the database the more resources they use. It would be economy not viable for most to host databases even anywhere close to that because 3TB is over $300 in storage costs a month along with bandwidth costs on the RDS instance it becomes very expensive to do so unless you have very good margins on your products and services.
Multiple RDS Instances
The work around to this problem is to use multiple RDS databases, I suspect that when a database gets to a certain size it becomes better to use multiple databases unless you use some kind of horizontal scaling which I believe SQL does not unless its MongoDB or similar.
http://aws.amazon.com/rds/aurora/, a custom MySQL from Amazon, supposedly 100% compatible and faster, will scale up to 64TB when released in final. Now in preview (5/2015).